Linear Polarizer Film

Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image.

When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).

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Glass polarizersprice

3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Polarizing filters reduce the light passed through to the film or sensor by about one to three stops (2–8×) depending on how much of the light is polarized at the filter angle selected. Auto-exposure cameras will adjust for this by widening the aperture, lengthening the time the shutter is open, and/or increasing the ASA/ISO speed of the camera. Polarizing filters can be used deliberately to reduce available light and allow use of wider apertures to shorten depth of field for certain focus effects.

Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

[What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?]

Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Thorlabs Polarizer

Much light is differentiated by polarization, e.g. light passing through crystals like sunstones (calcite) or water droplets producing rainbows. The polarization of the rainbow is caused by the internal reflection. The rays strike the back surface of the drop close to the Brewster angle.[6]

Example: A light ray is travelling in glass of refractive index, 1.5. It meets an interface with air (refractive index = 1.0) at an incident angle of 300. Find the angle of refraction.

This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

The benefits of polarizing filters are the same in digital or film photography. While software post-processing can simulate many other types of filter, a photograph does not record the light polarization, so the effects of controlling polarization at the time of exposure cannot be replicated in software.

Total Internal Reflection When a light beam is directed along the axis of a cylindrical glass fibre, it reflects repeatedly off the edges of the fibre, without appreciable loss. This kind of reflection is called Total Internal Reflection. To explain how it arises, we need to look at the refraction which occurs when light, which is travelling in a medium with higher refractive index, hits an interface with a medium of lower refractive index. Example: A light ray is travelling in glass of refractive index, 1.5. It meets an interface with air (refractive index = 1.0) at an incident angle of 300. Find the angle of refraction. In general, when a light ray from a higher refractive index medium enters a lower refractive index medium, then the ray bends away from the normal. Critical Angle When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Some companies make adjustable neutral density filters by having two linear polarizing layers. When they are at 90° to each other, they let almost zero light in, admitting more as the angle decreases.

Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image.

Glass polarizerscost

When a light beam is directed along the axis of a cylindrical glass fibre, it reflects repeatedly off the edges of the fibre, without appreciable loss. This kind of reflection is called Total Internal Reflection. To explain how it arises, we need to look at the refraction which occurs when light, which is travelling in a medium with higher refractive index, hits an interface with a medium of lower refractive index. Example: A light ray is travelling in glass of refractive index, 1.5. It meets an interface with air (refractive index = 1.0) at an incident angle of 300. Find the angle of refraction. In general, when a light ray from a higher refractive index medium enters a lower refractive index medium, then the ray bends away from the normal. Critical Angle When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

AmericanPolarizers

Use of a polarizing filter, in the correct direction, will filter out the polarized component of skylight, darkening the sky; the landscape below it, and clouds, will be less affected, giving a photograph with a darker and more dramatic sky, and emphasizing the clouds.[4] Perpendicularly incident light waves tend to reduce clarity and saturation of certain colors, which increases haziness. The polarizing lens effectively absorbs these light waves, rendering outdoor scenes crisper with deeper color tones in subject matter such as blue skies, bodies of water and foliage.[5]

Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection.

Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away.

1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object.

Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49.

2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Light reflected from a non-metallic surface becomes polarized; this effect is maximum at Brewster's angle, about 56° from the vertical for common glass. A polarizer rotated to pass only light polarized in the direction perpendicular to the reflected light will absorb much of it. This absorption allows glare reflected from, for example, a body of water or a road to be reduced. Reflections from shiny surfaces (e.g. vegetation, sweaty skin, water surfaces, glass) are also reduced. This allows the natural color and detail of what is beneath to come through. Reflections from a window into a dark interior can be much reduced, allowing it to be seen through. (The same effects are available for vision by using polarizing sunglasses.)

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6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

In this lecture the following are introduced: • Total internal reflection • Optical fibres • Image formation by convex lenses • Image formation by concave lenses

Some of the light coming from the sky is polarized (bees use this phenomenon for navigation[2]). The electrons in the air molecules cause a scattering of sunlight in all directions. This explains why the sky is not dark during the day. But when looked at from the sides, the light emitted from a specific electron is totally polarized.[3] Hence, a picture taken in a direction at 90 degrees from the sun can take advantage of this polarization. Actually, the effect is visible in a band of 15° to 30° measured from the optimal direction.

Linear polarizing filters can be easily distinguished from circular polarizers. In linear polarizing filters, the polarizing effect works (rotate to see differences) regardless of which side of the filter the scene is viewed from. In "circular" polarizing filters, the polarizing effect works when the scene is viewed from the male threaded (back) side of the filter, but does not work when looking through it backwards.

Glass polarizersamazon

The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high.

Critical Angle When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane.

Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Polarizer film

This kind of reflection is called Total Internal Reflection. To explain how it arises, we need to look at the refraction which occurs when light, which is travelling in a medium with higher refractive index, hits an interface with a medium of lower refractive index. Example: A light ray is travelling in glass of refractive index, 1.5. It meets an interface with air (refractive index = 1.0) at an incident angle of 300. Find the angle of refraction. In general, when a light ray from a higher refractive index medium enters a lower refractive index medium, then the ray bends away from the normal. Critical Angle When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

A polarizing filter or polarising filter (see spelling differences) is a filter that is often placed in front of a camera lens in photography in order to darken skies, manage reflections, or suppress glare from the surface of lakes or the sea. Since reflections (and sky-light) tend to be at least partially linearly-polarized, a linear polarizer can be used to change the balance of the light in the photograph. The rotational orientation of the filter is adjusted for the preferred artistic effect.

In general, when a light ray from a higher refractive index medium enters a lower refractive index medium, then the ray bends away from the normal. Critical Angle When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

For modern cameras, a circular polarizer (CPL) is typically used, which has a linear polarizer that performs the artistic function just described, followed by a quarter-wave plate, which further transforms the linearly polarized light into circularly-polarized light. The circular polarization avoids problems with autofocus and the light-metering sensors in some cameras, which otherwise may not function reliably with only a linear polarizer.

Circular polarizing photographic filters consist of a linear polarizer on the front, with a quarter-wave plate on the back. The quarter-wave plate converts the selected polarization to circularly polarized light inside the camera. This works with all types of cameras, because mirrors and beam-splitters split circularly polarized light the same way they split unpolarized light.[7]

From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

When a refracted angle equals 900 then a critical situation arises where the refracted ray travels along the interface. For typical glass with refractive index 1.5, this occurs when: For angles of incidence greater than the critical angle, the refracted ray does not exist, and the ray reflects off the interface at the same angle as it was incident. This reflection is called total internal reflection because there is no energy loss on reflection. The Silver reflecting surface in most domestic mirrors will absorb some of the incident light, so for them, multiple reflections will cause the image to fade away. Even though there is no energy loss in total internal reflection, the electric and magnetic fields of the light do penetrate a few wavelengths into the lower refractive medium. This wavelength penetration can be used to make variable-reflectance mirrors by placing another glass surface in near contact. This is known as frustrated total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

Polarizing filters can be rotated to maximize or minimize admission of polarized light. They are mounted in a rotating collar for this purpose; one need not screw or unscrew the filter to adjust the effect. Rotating the polarizing filter will make rainbows, reflections, and other polarized light stand out or nearly disappear depending on how much of the light is polarized and the angle of polarization.

Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges.

The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high.

4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane.

To couple light into optic fibres, the incoming light should be within a light cone that produces total internal reflection. This can be calculated by considering the geometry of the fibre core/envelope and the definition of the critical angle. Example: Calculate the largest angle of incidence available for light to be transmitted down an optic fibre which has core refractive index 1.50, and envelope refractive index 1.49. [What would happen if there was no cladding around the core (n1=1) and you tried to find the incident light cone for transmission by total internal reflection?] Optical Lenses Optical lenses work by refracting light rays. There are two main types of lens, "convex" and "concave". A convex lens will bring rays together. Its glass-in-air shape is (), i.e. it fatter at the middle than the edge. A concave lens has a "cave" or hollow. Its glass-in-air shape is )(, i.e. it is thinner at the middle than the edges. These are the four rays which you should be able to draw for a convex lens. 1 • Any ray through the centre of the lens will pass through undeviated. 2 • Any ray diverging from the primary focal point will emerge parallel to the axis 3 • Any ray parallel to the axis will converge to the secondary focal point. 4 • Any ray will converge to that point in the secondary focal plane, where a parallel ray through the centre intersects with the focal plane. These are the four rays which you should be able to draw for a concave lens. 5 • Any ray through the centre of the lens will pass through undeviated. 6 • Any ray parallel to the axis will diverge as if it came from the primary focal point. 7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

7 • Any ray converging towards the secondary focal point will emerge parallel to the axis. 8 • Any ray will diverge from that point in the primary focal plane, where a parallel ray through the centre intersects with the focal plane. Image formation by a convex lens 1 • Object inside the focal length. the image is virtual, upright & enlarged. 2 • Object between the focal length and twice the focal length. The image is real, inverted & enlarged 3 • Object greater than twice focal length. The image is real, inverted & diminished Image formation by a concave lens 4 • Real object The image is virtual, upright & diminished 5 • Virtual object The image is real, upright & enlarged The lens formula From similar triangles:      Also from different similar triangles:     Example An object 30mm high is placed 300mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is real (v is positive), inverted (m is negative), and enlarged (m is greater than 1). It is 600mm behind the lens and 30 x 2.0 = 60mm high. Example An object 50mm high is placed 100mm in front of a 200mm convex lens. Find the position, size and nature of the image. The image is virtual (v is negative), upright (m is positive) and enlarged (m is greater than 1). It is 200mm in front of the lens and 50 x 2.0 = 100mm high. Example An object is placed in front of a 120mm concave lens. The image is upright, 25mm high and -80mm from the lens. Find the position and size of the object. The object is real (u is positive), 240mm in front of the lens. Its size is 3x the image, i.e. 75mm high. Summarising: When light changes from a higher refractive index medium to a lower refractive index it bends away from the normal At the critical angle the refracted ray is at 900, i.e. parallel to the surface. and At incidence greater than the critical angle there is total internal reflection. Optical fibres have a protective envelope around them so that wavelength penetration does not produce any energy loss. Convex lenses are thicker at the middle than the edges. Concave lenses are thinner at the middle than the edges. There are four standard light paths for convex and concave lenses. The lens equations use the convention: real is positive (where minus means inverted).  Peter's Index   Physics Home   Lecture 7   top of page   Lecture 9  email Write me a note if you found this useful Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015

There are two types of polarizing filters readily available, linear and circular, which have exactly the same effect photographically. But the metering and auto-focus sensors in certain cameras, including virtually all auto-focus single-lens reflex cameras (SLRs), will not work properly with linear polarizers because the beam splitters used to split off the light for focusing and metering are polarization-dependent. Linearly-polarized light may also defeat the action of the anti-aliasing filter (low-pass filter) on the imaging sensor.