Polarization of light

This page explains the basics of light polarization and it's application to photography.

Polarization by reflection

As shown in the above picture, when non-polarized light (represented by arrows in all direction) travels from a transparent material (for example air, n₁ = 1.00) to another one with higher refraction index (for example glass, n₂ = 1.52), part of the light is refracted into the last material and part is reflected back into the first one.

If the angle of incidence is such that the reflected and the refracted rays are at 90° (which depends on the n₁ / n₂ ratio), then the incidence angle is called the "Brewster" angle and the reflected ray is linearly polarized parallel to the reflective surface. This is not valid for reflections on metallic surfaces.

If the angle of incidence is not exactly the Brewster angle the reflected ray will only be partially polarized.

The table below shows Brewster's angles for air-water and air-glass interfaces:

Material Refraction index Brewster angle

Air - Water n₁ = 1.00 ; n₂ = 1.33 37°

Air - Glass n₁ = 1.00 ; n₂ = 1.52 33°

Please remark that in this page angles are measured from the surface to the ray and not from the surface's normal axis to the ray which is usually used in optics.

This means that if we are at about 33° from a glass, the reflection from it will be polarized parallel to the glass surface. If we put a polarizer in front of our eyes (or our camera) we can remove the reflection if we turn the polarizer axis at 90° to the plane of polarization. The effect can be observed in the table below:

Picture of a window, no polarizer In this picture the camera is at about 33° from the glass of the window and this reflects the sky outside. The curtain behind the glass is barely visible. No polarizer has been used.

Picture of a window, verical polarizer This picture has been taken from the same position as above, but a linear polarizer has been installed in front of the camera. It has been oriented in order to let vertical polarized light go through and block horizontally polarized light. As one can see the reflection of the sky is still strongly present (which is composed by vertically polarized light, parallel to the vertical window) but the curtain behind the glass is much less visible: this is non-polarized light and is partially blocked by the polarizer. reflects the sky outside. The curtain behind the glass is barely visible.

Picture of a window, horizontal polarizer Same picture as above, but the polarizer has been rotated to let horizontally polarized light pass and block vertical. Now the reflection of the sky has almost disappeared and one can see the curtain behind the glass, which is non polarized light.

Polarization by scattering

When light scatters on a particle, some light is re-emitted in all directions, but light re-emitted in the plane perpendicular to the incident ray is polarized parallel to this plane, as shown in the above picture.

The blue color of the sky is caused by scattering of particles in the atmosphere, otherwise the sky should appear black. This is explained in the picture below. If we look at the sky when the sun is at 90° on our left hand or on our right hand the light we see is vertically polarized.

The effect can be observed in the table below:

Picture of the sky, no polarizer When this picture of the sky has been taken the sun was at about 90° on the right side. No polarizer has been used.

Picture of a window, vertical polarizer This picture has been taken as above but a vertical polarizer has been installed in front of the camera. Since the light from the sky is vertical polarized there is no great difference between this picture and the previous one.

Picture of a window, horizontal polarizer By rotating the polarizer by 90° to let only horizontally polarized light pass, part of the light from the sky is blocked making it appear deep blue. On the other hand, the clouds which emits non polarized light are still white, increasing the contrast.

Linear vs. circular polarizers

Two types of polarizer for SLR cameras can be found: linear and circular polarizers. What a photographer expects from a polarizer is a filter that blocks light which the polarization plane is not parallel to the one of the filter and lets in only one particular plane of polarization. For this a linear polarizer should be enough, but linear polarizers produce linearly polarized light which can fool the exposure meter of modern SLR cameras. In order to make the exposure meter work again a circular polarized filter is required. This filter is composed by a linear polarizer filter followed by a second filter that lets half of the light pass and turns the other half by 90° while delaying it by 90°. The result is actually circular polarized light, which will make the exposure meter think the light is non polarized. Circular polarizers work only in one direction.

If you are wondering how you can determine if your polarizer is linear or circular (and it's not written on it) is very easy: just look through it and turn it to see some polarization effect (for example try to make the reflection on a glass disappear, or try to darken the sky). If the filter works on both sides it's a linear polarizer and if it only works on one side it's a circular polarizer.

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Last update: 01/16/06

Material	Refraction index	Brewster angle
Air - Water	n₁ = 1.00 ; n₂ = 1.33	37°
Air - Glass	n₁ = 1.00 ; n₂ = 1.52	33°

	In this picture the camera is at about 33° from the glass of the window and this reflects the sky outside. The curtain behind the glass is barely visible. No polarizer has been used.
	This picture has been taken from the same position as above, but a linear polarizer has been installed in front of the camera. It has been oriented in order to let vertical polarized light go through and block horizontally polarized light. As one can see the reflection of the sky is still strongly present (which is composed by vertically polarized light, parallel to the vertical window) but the curtain behind the glass is much less visible: this is non-polarized light and is partially blocked by the polarizer. reflects the sky outside. The curtain behind the glass is barely visible.
	Same picture as above, but the polarizer has been rotated to let horizontally polarized light pass and block vertical. Now the reflection of the sky has almost disappeared and one can see the curtain behind the glass, which is non polarized light.

	When this picture of the sky has been taken the sun was at about 90° on the right side. No polarizer has been used.
	This picture has been taken as above but a vertical polarizer has been installed in front of the camera. Since the light from the sky is vertical polarized there is no great difference between this picture and the previous one.
	By rotating the polarizer by 90° to let only horizontally polarized light pass, part of the light from the sky is blocked making it appear deep blue. On the other hand, the clouds which emits non polarized light are still white, increasing the contrast.