Percentage of upolarized light

[ally1h]

Homework Statement

Unpolarized light is passed through a polarizer-analyzer combination. The transmission of the polarizer and the analyzer are at 30 degrees to each other. What percentage of the unpolarized light gets through the combination?

Homework Equations

The Attempt at a Solution

I am at a loss at to what to do. The only two equation I can think of, or find, that related to polarized light are the intensity equations: I = 1/2Io and I = Iocos^2(theta).

The answer according to my review packet is 37.5 degrees... I just don't know how to begin in order to get that answer. Will someone give me a few hints? Please?

 

[Redbelly98]

Let's start with the 1st polarizer. If Io is the initial intensity, what is the intensity after the 1st polarizer?

 

[thomate1]

I understand your confusion and I am happy to provide some guidance. In this scenario, we are dealing with polarized light, which means the light waves are oscillating in a single plane. The polarizer and analyzer are set at an angle of 30 degrees to each other, which means that the light passing through the polarizer will be partially blocked and only the component of the light oscillating in the same plane as the analyzer will pass through.

To solve this problem, we can use the equation for Malus' Law, which relates the intensity of transmitted light to the angle between the polarizer and analyzer. The equation is I = I₀cos²θ, where I₀ is the initial intensity of the unpolarized light and θ is the angle between the polarizer and analyzer.

In this case, θ = 30 degrees, so we can rewrite the equation as I = I₀cos²30. Using a calculator, we find that cos²30 = 3/4. Therefore, the percentage of unpolarized light that gets through the combination is 75% (or 0.75).

To find the percentage of unpolarized light that is blocked, we can subtract this value from 1 (since the total amount of light is 100%). So, the percentage of unpolarized light that is blocked is 25% (or 0.25).

I hope this helps! Remember, as a scientist, it's important to understand the concepts and equations behind a problem, rather than just memorizing numbers or equations. Keep practicing and you will become more comfortable with solving problems in polarized light.