There is a lot of interesting optics going on around us every day that we are often unaware of!  Some of these can be investigated with very simple and inexpensive tools, if one knows what to look for.  For instance: I’ve had a set of small polarized films sitting in my office for months.  The other day, I finally broke them out and, after some fiddling, it occurred to me that there are plenty of simple experiments that one can do with them!

Of course, to describe them, I should explain what “polarization” is!  It is a property that arises from the wave properties of light, specifically the transverse wave properties.  As I have noted a number of times on this blog, light may be described as an electromagnetic wave, with electric and magnetic fields being the quantities that “wave” as light travels, as illustrated below.

The most significant thing about this illustration is that is shows that the electric and magnetic fields “wiggle” in a direction perpendicular (or transverse) to the direction of wave travel — this is what is meant by a transverse wave.

However, this means that, for any particular direction of propagation, there are two distinct ways for the electric field of a light wave to oscillate, such as horizontal or vertical.  The direction that the electric field oscillates — horizontal, vertical, or anywhere in between — is what we call the state of polarization of the light wave.

We don’t usually notice polarization because direct sunlight and light from ordinary incandescent and fluorescent bulbs is unpolarized: it contains equal mixtures of horizontally and vertically polarized light.  However, a polarizing film such as those I have end up blocking light polarized along one direction while allowing light to be transmitted along the perpendicular direction.  We can therefore use these polarizers to play with light polarization and see what weird things can happen!

The simplest experiment is to demonstrate the behavior of crossed polarizers, i.e. what happens to light that attempts to pass through a pair of polarizers which are oriented perpendicular to one another.  This is shown in the video below.

So what’s happening? When the polarizers are aligned in the same direction, they block the same state of polarization, i.e. they both block horizontally polarized light, and both let the vertically polarized light through.  The second polarizer therefore has no effect on the light. When the polarizers are aligned perpendicular to one another, one will block the horizontally polarized light and the other will block vertically polarized light — no light at all gets through the pair!

For some experiments, it can be a little cumbersome to wield 2 or more polarizers plus a camera; fortunately, my flatscreen computer monitor already provides polarized light, as the following video illustrates!

Instead of using unpolarized sunlight as my light source and then filtering it with a polarizer, I can just use my screen as a source of polarized light.  This allows the next experiment, a classic, to be done with only three hands!

Starting with a polarizer in front of the screen tilted so that all of the light is blocked, we now insert a third polarized between the first two.  Intuitively, one would expect that no light gets through the system — polarizers 1 and 3 are perpendicular and would seem to block all the light — but this is not what happens.

If we insert the third polarizer between the polarized screen and the front polarizer in either the vertical or horizontal position, nothing happens.  But if we turn the polarizer 45° between, suddenly the light can pass through again!  What’s going on?

This takes a little bit more to explain, but is not too challenging.  The key comes in asking what actually happens to a polarized beam of light that is passed through a polarizer at an angle.   Let us suppose that the beam of light is horizontal and the polarizer allows light to pass at a 45° angle to the horizontal.  How do we determine how much light gets through the polarizer?  The trick is to note that a horizontal electric field can be rewritten as the sum of two perpendicular electric fields, one along 45° and the other along -45°.

 

In technical terms, the electric field is a vector, and it can always be interpreted as a sum of two other vectors.

For our purposes, this means that our horizontally polarized light may be written as a sum of +45° and -45° polarized fields.  When it encounters the polarizer, only the +45° component passes through, a fraction of the original field.  However — and this is the important part — the transmitted field is now polarized at +45°: the state of polarization has been changed by the polarizer!

The above process describes the first two legs of our experiment: horizontally polarized light (from our monitor) encounters a polarizer at +45°, and we now see that it comes out at +45°.  When it hits the third vertical polarizer, we can make a similar argument to describe what happens.  The electric field at +45° is equal parts horizontal and vertical polarization, and the vertical component can be transmitted.

 

In short, the key to the riddle is that polarizers don’t just block light, they change the state of the light that gets transmitted.  The middle polarizer allows light to be transmitted through the two perpendicular polarizers because it changes the state of the light from horizontal to 45°, allowing some to pass through the vertical polarizer.

How much light gets through a polarizer that is oriented at an arbitrary angle θ with respect to the light polarization?  The answer can be found from geometry, by drawing pictures similar to above; the result is what is known as Malus’ law.

Though direct sunlight and light from conventional bulbs is unpolarized, it turns out the same is not necessarily true of light reflected off of other objects.  As another simple experiment, one can look out the window at car windshields and see what happens.

Curiously, it seems that a given orientation of the polarizer will  block the reflected glare off of the car windshields and hoods!  Apparently, light becomes polarized when it reflects, but why?

The answer here comes from remembering that light is a transverse wave, i.e. that the electric field must be perpendicular to the direction of travel.  When unpolarized light reflects off of a surface, the part of the light whose electric field “pokes” into the surface will have an electric field that points mostly along the direction of the reflected wave.  But such a wave cannot exist, so most of that light gets transmitted into the material.  At a certain angle, known as the Brewster angle, all of that polarization gets transmitted, leaving only horizontally-polarized light.

 

There are two practical aspects to this observation.  First, in the early days of optics, experimenters would produce polarized beams of light by reflecting unpolarized light from a surface at the Brewster angle.  Until the invention of polarizers, this was the most reliable way to make polarized light.

The second practical aspect is in the design of polarized sunglasses!  Because a horizontal polarizer will block reflected glare off of cars, polarized sunglasses are designed to block this component of a light wave.

In fact, if you don’t want to spend the money to purchase polarizing films, you can perform these polarization experiments with a few pairs of polarized sunglasses instead!

The next experiment requires one extra piece of material, a piece of optical calcite.  They can be purchased for a few dollars from a scientific supply shop, though good quality polished pieces cost a bit more.

Optical calcite exhibits the curious phenomenon of double refraction, in which two images can be seen through the crystal, as shown for one of my samples below.

This double refraction is also due to polarization effects.  On an atomic level, calcite has a non-rectangular crystal structure.  This means that electric fields pointing in different directions in the crystal will have different interactions with the material, in a phenomenon known as birefringence.  When unpolarized light enters calcite, each component of the polarization therefore travels at a different speed and refracts differently at the surfaces, resulting in spatially separated images.

This means, however, that each image in a piece of calcite has a different polarization.  If we put a polarizer on top of the crystal, we can see this explicitly!

If you don’t have a piece of calcite on hand to examine birefringence, don’t worry — we can actually see it in a much more mundane item, a plastic cup, and in a much more spectacular way, as shown below.

The plastic cup looks quite normal under ordinary illumination, but when we put a polarizer in front of it, we suddenly see a rather lovely series of colors!  These colors persist even when the polarizer is rotated to block light coming from the screen — what is going on?

The plastic is exhibiting what is known as stress-induced birefringence.  In the process of molding, mechanical stress is “frozen” into the plastic that gives it an irregular atomic structure; this results in a small amount of birefringence.  The effect of this on light cannot be observed under natural or even polarized illumination; however, when we place the plastic between a pair of polarizers, we can see how the cup changes the polarization, much like the three polarizer experiment discussed earlier.  The color patterns arise because each wavelength of light is affected differently by the birefringent material.

This crossed polarizer method of observing stress-induced birefringence is actually a standard technique for looking for otherwise invisible stresses in manufactured products.

There’s one other experiment we can do with polarization that requires only a single polarizer, though we need to go outside to do it!  Holding up the polarizer to the sky, we can see that the blue sky itself is polarized!

The effect is much weaker than those we’ve seen previously; for comparison, I include still photos of the two polarizer orientations to see the difference.

 

Recall that I have said that direct sunlight is unpolarized; however, the blue sky is caused by sunlight reflecting (or, to use the more accurate term, scattering) off of molecules in the atmosphere.  In a manner similar to that by which we could get polarized light by reflecting sunlight off of a surface, the blue sky ends up being polarized because the scattering process that produces it is also polarization dependent.

Light observed coming directly from the sun or reflected off of the sky from directly opposite the sun is essentially unpolarized; light coming from directions between these two extremes is polarized.  The description of the polarization properties of light in the sky is known as the Rayleigh sky model. This polarization turns out to be a good navigational tool, and a number of insects are polarization sensitive because of it.

So: with a few pieces of cheap polarizers and crystals, we can perform a lot of investigations into the polarization of light!  Learning about the nature of light doesn’t always require the use of expensive tools and precision equipment.