# Unpolarized light of intensity I0 is sent through three polarizers. The axis of the second...

## Question:

Unpolarized light of intensity I0 is sent through three polarizers. The axis of the second polarizer is at an angle {eq}\Theta {/eq} to the first, and the axis of the third polarizer is at an angle {eq}\pi{/2} {/eq} to the first polarizer.

What is the transmitted intensity as a function of {eq}\theta {/eq} and its maximum possible value?

## Polarizers

Polarizers are special materials that output light with a single polarization direction. When unpolarized light is incident on a polarizer, half of its intensity will come out. When polarized light is incident on a polarizer, the intensity that comes out is given by Malus's law, which states that it is proportional to the cosine of the angle between the incident polarization and the polarizer squared. If a polarizer is at a 90-degree angle to the incident light's polarization, there will be no transmitted light, but if another polarizer is put between them at another angle there will be some light that can be transmitted.

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{eq}I = \frac{I_0}{8}\sin^2(2\theta) {/eq}

The first polarizer will transmit half of the incident light, and the second two polarizers will transmit...