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The figure shows a horizontal, unpolarized ray of light incident on a block labeled birefringent crystal. The ray is perpendicular to the face of the crystal where it enters it. The incident ray splits into two rays when it enters the crystal. One part of the ray continues straight on. This ray is horizontally polarized. The other part of the ray propagates at an. This ray is vertically polarized. The second ray refracts upon leaving the crystal such that the two rays are parallel outside the crystal. The rays are labeled as two perpendicularly polarized beams.
Birefringent materials, such as the common mineral calcite, split unpolarized beams of light into two with two different values of index of refraction.


  • Polarization is the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave. The direction of polarization is defined to be the direction parallel to the electric field of the EM wave.
  • Unpolarized light is composed of many rays having random polarization directions.
  • Unpolarized light can be polarized by passing it through a polarizing filter or other polarizing material. The process of polarizing light decreases its intensity by a factor of 2.
  • The intensity, I , of polarized light after passing through a polarizing filter is I = I 0 cos 2 θ , where I 0 is the incident intensity and θ is the angle between the direction of polarization and the axis of the filter.
  • Polarization is also produced by reflection.
  • Brewster’s law states that reflected light is completely polarized at the angle of reflection θ b , known as Brewster’s angle.
  • Polarization can also be produced by scattering.
  • Several types of optically active substances rotate the direction of polarization of light passing through them.

Key equations

Speed of light c = 2.99792458 × 10 8 m/s 3.00 × 10 8 m/s
Index of refraction n = c v
Law of reflection θ r = θ i
Law of refraction (Snell’s law) n 1 sin θ 1 = n 2 sin θ 2
Critical angle θ c = sin −1 ( n 2 n 1 ) for n 1 > n 2
Malus’s law I = I 0 cos 2 θ
Brewster’s law tan θ b = n 2 n 1

Conceptual questions

Can a sound wave in air be polarized? Explain.

No. Sound waves are not transverse waves.

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No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

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Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Energy is absorbed into the filters.

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When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to 1 λ . Does this mean there is more scattering for small λ than large λ ? How does this relate to the fact that the sky is blue?

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Using the information given in the preceding question, explain why sunsets are red.

Sunsets are viewed with light traveling straight from the Sun toward us. When blue light is scattered out of this path, the remaining red light dominates the overall appearance of the setting Sun.

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When light is reflected at Brewster’s angle from a smooth surface, it is 100 % polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be 100 % ?

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If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well. Why not?

The axis of polarization for the sunglasses has been rotated 90 ° .

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What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

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