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

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

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

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.

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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.

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 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.

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

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

Understanding the fundamental parameters of laser sources is crucial in harnessing their capabilities effectively. In this context, we will explore three key parameters: average power, pulse width, and pulse energy, each of which plays a distinct role in laser technology.

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.

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

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.

Concave lenses have total internal reflectionbrainly

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.

These parameters are integral in optimizing laser processes and ensuring desired outcomes in various applications, making a thorough understanding of average power, pulse width, and pulse energy essential in laser technology.

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.

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

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

Pulse width, symbolized as τ (tau), signifies the duration of a laser pulse. It measures the time it takes for the laser to emit its peak energy during a pulse. Pulse width is typically expressed in units of time, such as seconds or milliseconds. In laser technology, pulse width is pivotal for precision and control, especially in applications where short, precise bursts of energy are needed, like laser ablation, material removal, and some medical procedures.

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.

Peter's Physics Pages  Peter's Index   Physics Home   Lecture 7   Course Index   Lecture 9  An Introductory Physics Course with Peter Eyland Lecture 8 (Optical fibres & lenses)

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

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

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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

Concave lenses have total internal reflectionquizlet

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

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.

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

Average power, denoted as P_avg, is a fundamental parameter that characterizes a laser's ability to deliver a consistent and sustained level of energy over time. It measures the laser's output power averaged over a specified time duration, typically expressed in watts (W). Average power is particularly relevant in applications where a continuous and stable energy source is essential, such as laser cutting, welding, or continuous-wave (CW) laser processes.

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

[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?]

Laser sources are devices that generate and emit highly concentrated, coherent, and often monochromatic light or electromagnetic radiation through a process called stimulated emission. The term "#laser" stands for "Light Amplification by Stimulated Emission of Radiation." Lasers find widespread applications in various fields, including materials processing, medical procedures, scientific research, telecommunications, and more.

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

Pulse energy, represented as E_pulse, quantifies the total energy contained within a single laser pulse and is typically measured in joules (J). Pulse energy is crucial for applications that rely on the laser's ability to create an impact, such as laser material processing, scientific experiments, and some medical procedures. It is calculated by multiplying the laser's average power by the pulse width (E_pulse = P_avg * τ) and determines the strength of each individual pulse.

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).

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

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

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

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

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