Lets look at what 18-55mm means first. The numbers before the ”mm” relate to the focal length of the lens. Essentially, focal length means what you are going to be able to see when you look through the viewfinder. (Ever looked through the lens and everything looked closer than it actually was, or further away? That is your focal length - you can see a full comparison of different focal lengths here)  The important thing for you to know is that the lower the focal length (smaller the number) the wider the view - i.e. you will be able to see more in your image.

So when you see the focal length numbers of a lens, the first thing you are probably going to want to know how this is going to look compared to ”real” life.  This will be different depending on whether you have a cropped frame camera like the Rebel or a full frame camera like the 6D. I’m going to start with explaining the full frame because it is the easiest to understand.

I've covered a fair bit on lenses this past week, comparing different focal lengths and understanding lens compression, and I thought I'd rewind a bit for any new photographers, and talk about what the numbers on the lens mean.

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Please note there is a lot more technical mathematical stuff to it than that,  but I think as long as we know what we can do with the lens once it’s on our camera, that’s all we really need to know!

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While optical activity usually results from the presence of chiral molecules, with a concentration difference between the two possible enantiometers, it can also be induced by a magnetic field in a substance which is not naturally optically active. That is called the Faraday effect, and is exploited in Faraday rotators and Faraday isolators.

A circular polarization state can mathematically be obtained as a superposition of electric field oscillations in the vertical and horizontal direction, both with equal strength but a relative phase change of 90°. Effectively, this leads to a rapid rotation of the electric field vector – once per optical cycle – which maintains a constant magnitude.

In the simplest case, a light beam is linearly polarized, which means that the electric field oscillates in a certain linear direction perpendicular to the beam axis, and the magnetic field oscillates in a direction which is perpendicular both to the propagation axis and the electric field direction. The direction of polarization is taken to be the direction of the electric field oscillations (i.e., not the magnetic ones). For example, a laser beam propagating in <$z$> direction may have the electric field oscillations in the vertical (<$y$>) direction and the magnetic field oscillations in the horizontal (<$x$>) direction (see Figure 1); it can be called vertically polarized or <$y$>-polarized. In a different perspective, this is also shown in the second part of Figure 2.

Note that radial or azimuthal polarization state requires a zero electric field strength and thus also a vanishing optical intensity on the beam axis; it is not compatible with a Gaussian beam, for example. Radially polarized beams frequently exhibit a kind of donut profile.

On a full frame, a focal length of 50mm will ”see” roughly the same view as you do with your naked eye. Remember this, because when you look at the focal length of a particular lens you will be able to tell whether this will give you a view that will include more in the frame or less. If the lens has a higher number than 50mm for the focal length, like 85mm, you will see less through the frame and it will look more ”zoomed” in. If it has a lower number, like 35 mm, the more you will see in the frame.  Look at the images above again for a comparison.

The degree of linear polarization is often quantified with the polarization extinction ratio (PER), defined as the ratio of optical powers in the two polarization directions. It is often specified in decibels, and measured by recording the orientation-dependent power transmission of a polarizer. Of course, the extinction ratio of the polarizer itself must be higher than that of the laser beam.

Fully polarized states can be associated with points on the so-called Poincaré sphere. Partially polarized states correspond to points inside that sphere; unpolarized light is represented by the point at its center.

Circularlypolarized light

If the oscillations of the horizontal and vertical electric field vector do not have the same strengths, one has the case of an elliptical polarization, where the electric field vector, projected to a plane perpendicular to the propagation direction, moves along an ellipse.

It’s a zoom lens, with a focal length range of 24 - 75mm. As I said, if I multiply these numbers by 1.6, I get the equivalent for a cropped camera which is 39 - 120mm.  You can see by doing this just how differently this lens will perform on a full frame or a cropped frame camera!  (Again, bear in mind that I am talking about lenses made for a full frame camera, not lenses specifically designed for a crop frame)

I would have been glad to finally remove a serious mistake, but I believe my equations are correct. They agree with those in various textbooks and e.g. also in Wikipedia. Your argument concerning energy swapping back and forth between electric and magnetic fields looks somewhat plausible but is not accurate.

A light beam is called unpolarized when the analysis with a polarizer results in 50% of the power to be in each polarization state, regardless of the rotational orientation. Microscopically, this usually means that the polarization state is randomly fluctuating, so that on average no polarization is detected. Note that such fluctuations are not possible for strictly monochromatic light.

Polarization

In the previous cases, the direction of the electric field vector was assumed to be constant over the full beam profile. However, there are light beams where that is not the case. For example, there are beams with radial polarization, where the polarization at any point on the beam profile is oriented in the radial direction, i.e., away from the beam axis.

50mm is a good all rounder, 35mm and under is great for landscapes or lifestyle photography where you want to be able to fit more into the frame (great for shooting indoors) and 85mm and above are great for portraits.

The polarization state of monochromatic light is often described with a Jones vector, having complex electric field amplitudes for <$x$> and <$y$> direction, if propagation occurs in <$z$> direction. That Jones vector may be constant over some area across the beam, or it may vary, for example for a radially polarized beam (see above). The effect of optical elements such as waveplates, polarizers and Faraday rotators can be described with Jones matrices, with which the Jones vectors can be transformed by multiplication. (One assumes a linear relationship between input and output amplitudes.) A whole sequence of such optical elements can be described with a single Jones matrix, which is obtained as the product of the matrices corresponding to the components.

It only has one number before the mm, which means it is a ”fixed” or ”prime” lens - it does not zoom and has a fixed focal length. The 50mm means that it sees the same as the naked eye on a full frame but on a cropped frame, it is going to behave more like an 85mm (50mm x 1.6) and make everything look a bit closer than it actually is, and it’s a good portrait length. There’s only one F number - F1.4, which is the lowest aperture setting this lens can go to, which is nice and low so I can get lots of nice light into my camera!

A radially polarized laser beam may be generated from a linearly polarized beam with some optical element, but it is also possible to obtain radially polarized emission directly from a laser. The advantage of this approach, applied in a solid-state bulk laser, is that depolarization loss may be avoided [4]. Furthermore, there are applications benefiting from radially polarized light.

There are also azimuthally polarized beams, where the electric field direction at any point is tangential, i.e., perpendicular to a line through the point and the beam axis.

Of course, the polarization can have any other direction perpendicular to the beam axis. Note that a rotation of the polarization by 180° does not lead to a physically distinct state.

One distinguishes left and right circular polarization (see Figure 2). For example, left circular polarization means that the electric (and magnetic) field vector rotates in the left direction, seen in the direction of propagation. For an observer looking against the beam, the rotation of course has the opposite direction.

So, this particular lens has an aperture range of 3.5 to 5.6. If you have two numbers (like this one) separated by a dash, this means that the aperture changes with the focal length of the zoom. Use the lens at 55mm and you will have a maximum aperture of 5.6. At 18mm,  the maximum aperture will be F3.5. The particular aperture range of this lens doesn’t go nearly as low as I want it to go to let lots of yummy light into my camera and get the nice creamy backgrounds I’m looking for (You want at least F2.8)- so I know that this isn’t the lens for me.

Jones vectors can be used only for fully defined polarization states, not for unpolarized or partially polarized beams (see below) having a stochastic nature.

This was one of my very first questions I had when buying my DSLR and it took me a little while to figure out! Hopefully this post will help break this down if you are new to lenses too.

You will also note it only has one F number - that is because you can use F2.8 throughout the whole focal range – it doesn’t change as you zoom in and out.  This is called a fixed aperture zoom, and therefore combines the benefit of a zoom, with a lower aperture to let lots more yummy light into the camera.

For example, if I put a standard 50mm lens (one made for a full frame like most prime lenses are) on a cropped body camera, instead of the scene through my viewfinder being the same as the naked eye, it will actually look a lot closer - more like how an 85mm would perform on a full frame.  This is to all to do with the size of the sensor being different.

There are cases where polychromatic light can be described with a single Jones vector, since all its frequency components have essentially the same polarization state. However, the polarization state is substantially frequency-dependent in other cases.

Let’s move on the next set of numbers, which if you remember, was f/3.5-5.6. This refers to the aperture range of the lens and is lovely and simple to explain. Aperture is basically how big the opening in your lens is when you take your picture. The size of this opening is measured in f/stops. The smaller the number, the wider the opening and therefore the more light gets into your camera.

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Polarization oflight

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All you need to do is multiply the focal length by a ”crop factor” to see how it compares to the full frame. For a Canon Rebel, the crop factor is 1.6 (so if I used a Canon 50mm F1.8 lens, this gives me the around 80mm - so behaving more like a 85mm as I said above)

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Quite simple so far, but this is where it gets a bit more complicated. If you are just starting out, you probably don’t have a full format camera, you will have a cropped frame, and this makes a world of difference to how the focal length ”performs” on your camera.

On the other hand, the polarization state of the laser output can be disturbed e.g. by random (and temperature-dependent) birefringence, such as occurs e.g. in optical fibers (if they are not polarization-maintaining or single-polarization fibers) and also in laser crystals or glasses as a result of thermal effects (→ depolarization loss). If the laser gain is not polarization-dependent, small drifts of the birefringence may lead to large changes of the polarization state, and also a significant variation in the polarization state across the beam profile.

There are also partially polarized states of light. These can be described with Stokes vectors (but not with Jones vectors). Further, one can define a degree of polarization which can be calculated from the Stokes vector and can vary between 0 (unpolarized) and 1 (fully polarized).

It can take a little while to get your head around the numbers, so I hope this helped a bit with learning what the lens numbers mean and how to decide whether the lens is right for you.

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polarization中文

So, now you can apply this knowledge to other lenses to work out what they mean. Lets look at a couple more.....(these are all lenses that are meant for a full frame, just to avoid any confusion!)

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The polarization state of light often matters when light hits an optical surface under some angle. A linear polarization state is then denoted as p polarization when the polarization direction lies in the plane spanned by the incoming beam and the reflected beam. The polarization with a direction perpendicular to that is called s polarization. These indications have a German origin: s = senkrecht = perpendicular, p = parallel.

Elliptical polarization

Note that a very small gain or loss difference for the two polarization directions can be sufficient for obtaining a stable linear polarization, provided that there is no significant coupling of polarization modes within the laser resonator.

What I can work out from this is that in order to get the same view on a cropped body as I would see with the naked eye, I would need around about a 30mm focal length. (30mm x 1.6 = 48mm)

Your first plot shows the magnetic and electric field in phase – which is wrong. The magnetic field is made from the changing electric field. The two fields swap energy back and forth. Hence the magnetic field is at a maximum when the electric field has the largest rate of change, that is, at zero E field. The magnetic field zeros in strength when the electric field rate of change is zero, at it's peak. These are a simple consequence of Maxwell's Equations and is covered in most any text on E&M. The worst error I have found in years of use of your marvelous resource!

Electric polarization

Linearly polarized light can be depolarized (made unpolarized) with a polarization scrambler, which applies the mentioned random polarization changes, or at least quasi-random changes.

In many respects, light can be described as a wave phenomenon (→ wave optics). More specifically, light waves are recognized as electromagnetic transverse waves, i.e., with transverse oscillations of the electric and magnetic field.

The higher the focal length (bigger number) the less of your image you will see, in other words it will look more zoomed in. I’m quite a visual person so here are a couple of examples of some different focal lengths in practice (I’m sitting in the same place for all 3)

Different cameras have different sized crop sensors, so you need to know your particular model’s ”crop factor” - Canon’s is 1.6, but Nikon’s is 1.5. As usual DPS have a brilliant article which gives you all the information at a glance here. It also includes a table that shows the equivalent lens sizes for the different crops factors.

As explained above, a waveplate or other birefringent optical element may rotate the direction of linear polarization, but more generally one will obtain an elliptical polarization state after such an element. True polarization rotation, where a linear polarization state is always maintained (just with variable direction), can occur in the form of optical activity. Some optically active substances such as ordinary sugar (saccharose) can produce substantial rotation angles already within e.g. a few millimeters of propagation length. Optical activity can be accurately measured with polarimeters.