Polarization

Jan 9, 2020 — (ii) Focal length of a concave mirror. The focal length of a concave mirror is the distance between its pole and the principal focus.

In theory, magnification is unlimited. However, since it is related to the aperture of the optics, there are limits. The exit pupil also plays an important role. This is the diameter of the beam of light that leaves the eyepiece and enters the eye. We’ll come to this again later.

More magnification equals a better telescope? Beginners often think this, but it is not the determining factor, small or medium levels of magnification are usually more effective. Here you can learn how to calculate magnifications.

Each telescope has its own magnification limit. It is equivalent to 2 times the lens aperture. However, you cannot and should not use this upper limit every night. This is because you will only enjoy observing if the object is bright enough and the seeing is perfect. It is easy to find out for yourself whether it makes sense to operate at this limit: use an eyepiece with a 0.5mm exit pupil and pay attention to the seeing. How does the object appear? Is it blurred? Is it too dark? How are the conditions tonight?

Magnification depends on the ratio of the telescope's focal length to the focal length of the eyepiece. To calculate this, divide the focal length of the telescope (ft) by the focal length of the eyepiece (fe):

Minimum magnification is limited by the telescope’s aperture. Here, the exit pupil should not be larger than seven millimetres. This is usually also the maximum diameter that the pupil of the human eye can reach. But this is only possible at night and in absolute darkness.

Unfortunately, no telescope nor any other optical instrument is completely defect-free. Here we describe the most important image defects found in astronomical telescopes.

For example, a 4" telescope has a minimum magnification of 14x. An 8" telescope has a minimum of 29x, and a 14" telescope has a minimum of 50x. Below the ...

My doubt comes from a discussion we had in class about the Brewster angle, glare effect produced by the reflection of sunlight on water and polarizing sunglasses.

Note regarding glare and sunglasses and the Brewster angle: You have pointed out that unpolarized light incidence at (or near) the brewster angle will be filtered and (mostly) s-polarized upon reflection. If the surface under consideration is horizontal (asphalt on the road, or standing water, for example) then we know that s-polarized light is h-polarized light. Thus if we want to filter this out using sunglasses for example we should make the sunglasses eliminate h-polarized light. Polarizing sunglasses are designed to eliminate h-polarized light when the wearer is standing upright and holding their head in the usual way. If they tilt their head, however, then their sunglasses will now let in more h-polarized light and allow in more v-polarized light. The angle of the sunglasses defines a new coordinate system. Note also that if the surface is vertically oriented (such as the rear window of the car in front of you) then since sunlight is typically coming from above, the s-polarized reflected light will again be mostly horizontally polarized. This means that generally polarizing sunglasses are good and reducing glare from all sorts of objects assuming the sunlight is coming from above. However, during sunrise and sunset the sun is lower in the sky so the reflected s-polarized light may now have large components in the vertical direction so the sunglasses will not work as effectively.

Electricpolarization

Politicalpolarization

I put the tilde on the p to v comparison because for glancing angles (where the light is travelling almost horizontal, large angle of incidence) it makes sense to talk about vertical polarized light but if the light is travelling more and more perpendicular to the surface (smaller angles of incidence) it makes less and less sense to talk about vertically polarized light.

s and p are defined with respect to the plane of incidence as described in the Wikipedia article. The plane of incidence is defined by two vectors. One vector is the normal vector to the surface (the vector which points out of the surface). The other vector is the direction of propagation for the light under consideration. Often these two vectors are not parallel and thus they describe a plane*. This plane is called the plane of incidence.

H and V polarization usually refer to some arbitrary reference frame. This reference frame is usually defined by the direction of gravity (call this $\hat{z}$ direction). If light is travelling "horizontally" (meaning perpendicular to the direction of gravity, for example in the $\hat{y}$ direction) then we can talk about horizontally and vertically polarized light. For vertically polarized light the electric field is parallel to the direction of gravity so it is in the $\hat{z}$ direction. For horizontally polarized light the electric field is perpendicular to the direction of gravity, that is in the $\hat{x}$ direction. Note that in both cases the electric field is perpendicular to the direction of light propagation.

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Circularpolarization

For example, if you have a telescope with a focal length of 1,000 mm and an eyepiece with a focal length of 5 mm, you'll get 200 times magnification.

So an unpolarized electromagnetic wave as light when incident on an interface air-water will be reflected as an "s" polarized light at the Brewster angle. This means it oscillates on a plane perpendicular to the plane of incidence, hence parallel to the surface? If yes, then can we say that an s-polarized light is equivalently said to be horizontally polarized?

Single-order diffraction for such a period occurs at the Littrow angle of θL = arcsin(1/3) ≅ 20º. PGL Technical Note – The Grating Equation. PDF of this ...

50), and discriminant validity via Fornell-Larcker criterion and HTMT) met the requirement. Because we treated actual usage of WWD as a second-order ...

A telescope creates a focal point, depending on the curvature of the mirrors or lenses. With the focal length alone, a small level of magnification will be achieved. But in order to be able to look at the image, you additionally need an eyepiece. Imagine an eyepiece as a magnifying glass which enlarges the image at the focal point.

Maximum useful magnification is reached with an eyepiece exit pupil of 0.7 mm - 0.8 mm. It is not a precisely defined limit, more a guide for optimum magnification.

\begin{align} p\text{-polarized} & = \text{vertically polarized}\\ s\text{-polarized} & = \text{horizontally polarized} \end{align}

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Linearpolarization

*However for the case of light which is shining directly incident onto a material surface the two vectors are parallel and no plane is defined. I'll discuss this case shortly.

Divide the telescope's aperture by the diameter of the maximum aperture of the eye’s pupil, to get the minimum useful magnification.

Circularly polarized light

Finally to unite all of these concepts. We see that horizontal and vertical polarization refer to the direction of polarization compared to the direction of gravity and s and p-polarization refer to the direction of polarization compared to the plane of incidence. If the surface normal is pointing either in the direction of gravity (as implied by the figure in the OP) or perpendicular to the direction of gravity (a surface which is vertical like a mirror in the restroom) then there is a relationship between s and p-polarized and horizontal and vertically (h and v) polarized light.

If that's the case then sunlight (unpolarized light) will be reflected as horizontally polarized so to reduce glare effects the polarizing sunglasses must block the horizontal direction of polarization, right?

p-polarized light is light where the electric field vector lies in this plane of incidence. s-polarized light is light where the electric field vector is perpendicular to this plane of incidence. If you think about this in terms of the material surface you can see that the electric field vector either pokes in or out of the material surface for p-polarized light while it "lies flat" in the plane of the material surface.

A telescope with an aperture of 100 mm would therefore have a optimum magnification of 142-times and a 200 mm telescope of 285-times.

There are three important magnifications that every amateur astronomer can easily determine. Here we show you how you do this.

If the electric field is directly incident on the surface the propagation direction and surface normal are parallel so we cannot define a plane of incidence. In this case all polarizations "lie flat" in the plane of the material surface so it is sort of like all polarizations are "s-polarized". This is comparable to the case when light was travelling directly upwards against gravity and all polarizations looked like horizontal polarizations so it didn't make sense to talk about horizontal and vertically polarized light anymore. In this case we must introduce a new different reference frame if we want to talk about the polarization of the light field.

Optimum magnification or maximum useful magnification is reached when a star no longer appears point-shaped, but as a tiny disk with diffraction rings. At this point, you are using all the optics’ available resolving power. This means that you can see many details that remain hidden at a lower or higher magnifications.

polarization中文

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Ellipticalpolarization

A practical example: if you are using a telescope with 200 mm lens aperture, the minimum useful magnification is around 28 times. If the telescope aperture was larger, the minimum magnification must be higher. For a smaller telescope, it is correspondingly smaller.

However, imagine a beam travelling directly upwards from the ground in the $\hat{z}$ direction. In this case the polarization lies in the $\hat{x}$, $\hat{y}$ plane. It doesn't make sense to me to call either of these vertical polarization. Rather, we would be better served calling them "East-West" and "North-South" polarized, for example. The key point here is the geometric and coordinate dependent nature of how we call polarizations.

The Field of View (FoV) is the diameter of the circle of light that you see when looking into a microscope. The higher your magnification, the smaller the ...

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Due to diffraction of light, conventional microscopy has a practical resolution limit of ∼ λ / ( 2 N A ) , called the Abbe diffraction limit, where λ is the ...

This definition of horizontal and vertical polarization also makes sense for light travelling at some reasonable angular deviations from the horizontal plane. We can talk about polarizations which mostly don't have components in the $\hat{z}$ direction, horizontal polarizations, and polarizations which mostly do have components in the $\hat{z}$, vertical polarizations.

s and p polarizations are different from horizontal and vertical polarizations. As described above, horizontal and vertical usually refer to the direction of the electric field with respect to gravity. s and p polarizations are instead defined with respect to a reference frame which is related to the surface with which the light is interacting. The surface can be oriented in an arbitrary direction with respect to gravity so we see that s and p are unrelated to horizontal and vertical polarization.

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