Question

A series of polarizers are each placed at a 13° interval from the previous polarizer. Unpolarized light is incident on this series of polarizers. What will be the intensity of the light after passing through the series of polarizers?

1) The intensity of the light will decrease exponentially with each polarizer
2) The intensity of the light will remain constant after passing through the series of polarizers
3) The intensity of the light will increase with each polarizer
4) The intensity of the light will decrease linearly with each polarizer

Answer 1

The intensity of light will decrease exponentially after passing through a series of polarizers placed at a 13° interval from each other due to the cosine squared dependence of the transmitted intensity on the angle between the polarizers.

Step-by-step explanation:

The intensity of light after passing through a series of polarizers will decrease exponentially with each polarizer when they are placed at an angle to each other. As unpolarized light passes through the first polarizer, it becomes polarized, and its intensity is reduced by half. As it passes through the subsequent polarizers at a 13° interval, the intensity I of the light can be described by the formula I = Io cos²(θ), where Io is the initial intensity and θ is the angle between the direction of polarization of the light and the axis of each polarizer relative to the first. Because of the cosine squared dependence and the fact that θ is different from 0° (parallel) or 90° (perpendicular), the intensity will decrease by a factor that is less than 1 for each polarizer it passes through, leading to an exponential decrease overall. Therefore, option 1 is the correct answer: The intensity of the light will decrease exponentially with each polarizer.