Experimenting and understanding polarizing filter

This post will not be about physical basics of polarized light or polarization in general. For this information look at other places on Internet, like: Wikipedia, Physics Classroom or tons of other sources.
Instead, I will try to explain when polarized light in combination with a polarizing filter can be efficiently used for photography. But knowing at least some physics is helpful for proper understanding and usage of polarized light.

Some physical background

The most important to understand is to realize that polarizing filter is able to regulate amount of polarized light which reaches the camera's lens, and consequently, the sensor. To regulate the amount of polarized light reaching the sensor one have to rotate the filter until the requested effect is achieved. 

Unpolarized light reaching the lens will be slightly reduced (due to the imperfectness of filter), but the effect will be the same for the whole scene, disregard the filter orientation.

Natural light generated by sun is unpolarized. Artificial light sources also produce unpolarized light.

So, the first question to answer is how the polarized light is created? There are two (sometimes three) important sources of such light for photographers:

- reflection of light

- scattering of light

- refraction of light

In other words with polarizing filter, one can regulate amount of reflected, scattered (or refracted) light reaching the camera's sensor. 

The problem is that it is too generic to make practical use of it. Not all kinds of reflection or scattering will create polarized light, hence an environment where polarizing filter could be applicable. Let's start by showing the situations where using of polarizing filter doesn't make sense at all.

Reflections - when a polarizing filter does not have effect

First of all, light reflected perpendicularly from the reflecting surface is not polarized. According to polarization physics, reflected perpendicular light is not polarized. So in the scenario shown in the picture below using polarizing filter will not work:

For the demonstration purposes I was photographing the interior of a room from outside, standing in front of the window. My silhouette (and the trees in the background) can be seen as a source of light. Since it is perpendicular to the reflecting surface (the window), the reflected light is not polarized and the filter will not have any effect.

Another case are the reflections from the metallic surfaces. Metal surfaces don't polarize light.

Maximize effect of polarizing filter

Another extreme is the situation when the reflected light is fully polarized. In such case we can use the filter to its full extent. It has been discovered by Scottish scientist, David Brewster, that for a given light reflected from non metallic, transparent surface, there is an angle of incidence that results in perfectly polarized reflected light. This angle, called Brewster's angle is dependent on the reflecting material.

For glass it is 53.6 degrees, for water 53.1 degrees.

Let's see what it means from the photographer's point of view:

When one places the camera as on the picture above and composes to have the central object in the middle of the scene, this object will be most visible. The other will be covered (at least partially) by reflected light. A more practical example. First, the pool has been photographed without polarizing filter. It reflects basically everything:

Now with the polarizing filter set to maximally reduce reflections.

 Note that the leaves in the pool (at the bottom and in the middle) became visible and reflection in this area is eliminated almost completely. However at the edges of the pool I still have the reflected clouds and trees. It is because the reflected light outside the Brewster angle is only partially polarized, hence partially eliminated by the filter.

This simple experiment shows another important aspect of using the polarizing filter. Typically, when using in landscape photography its effects will be limited to some elements of the scene only. 

Which surfaces cause polarization?

In general, all non-metalic surfaces reflecting light introduce some degree of polarization. So organic substances (leaves, wood, mushrooms, etc.) will 'produce' polarized light:

Scene photographed without polarizing filter

Scene with polarizing filter

Without polarizing filter

With polarizing filter

Note that using polarizing filter can result in more saturated colors.

Another source of polarization - scattered light

The light travelling through atmosphere gets scattered by the molecules the atmosphere consists of. Effect of scattering manifests to us in blue color of the sky during the day. It turns out that light scattered through atmosphere is also partially polarized. Which means we can reduce its amount by the polarizing filter. It results in the darker sky in the picture (and is by the way a 'selling feature' of many filter manufacturers):

First picture was taken without the filter, the other with it, set to maximum effect. The difference in the sky is obvious.

But 'darkening the sky' is just one application. We can see the polarizing filter in such scene as a 'compressor' of the scene dynamic range. Since sky gets darker, the exposure can be adjusted to let darker elements (like the trees in the above scene) to 'pop up':

The photo above was taken with polarizing filter set for maximal effect for the sky, but the exposure has been increased by 3 stops. Both trees are much lighter and sky has still pleasant, blue color. I lost some details in the clouds on the left side, but the contrast between the sky and the trees is reduced.

Final notes

Polarizing filter requires some practice. But knowing the physical basics of its work helps to master it quickly by avoiding unnecessary experiments. Here short summary:

- Light perpendicular to the reflecting surface is not polarized. So polarizing filter will not help there,

- There is a family of angles for the reflected light (around 53 degrees for water and glass), where the effect of polarizing filter is the strongest,

- For landscape photography the effect of filter will me most often local, limited to some elements of the scene,

- Due to the technical limitations polarizing filters reduce the light for the whole scene. Depending on the filter type the reduction varies between 1 and 3 stops.

- Polarizing filter can be used for 'darkening the sky' but also to compress the dynamic range of the scene involving the sky.