Intensity of the incident light

[vrobins1]

Homework Statement

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of 33.0° with respect to the first and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from the system has an intensity of 2.3 W/m2, what is the intensity of the incident light?

Homework Equations

I_out=I_incos²$$\theta$$

The Attempt at a Solution

I know that after I₀ passes through the first polarizer, it is 1/2I₀. After it passes through the second, I thought it would be 1/2I₀cos²(33), and after it passes through the third, 1/2I₀cos²(33)cos²(45).
This would all equal 2.3, which I was given.
So I set up my final equation as:
1/2I₀cos²(33)cos²(45) = 2.3, or
I₀= 2.3 / (1/2cos²(33)cos²(45).

I solved and got 13.08, but that is incorrect. Can anyone offer any insight? Thanks.

 

[Redbelly98]

For the third polarizer, use the angle between it and the second polarizer.

45° is the angle between the third and first polarizer.

 

[nlightner]

Your approach is correct, but there is a small mistake in your equation. The intensity of the incident light should be equal to the intensity of the light after passing through all three polarizers, so your final equation should be:

I0 = 2.3 / (1/2cos2(33)cos2(45))^2

This will give you the correct answer of approximately 13.08 W/m2.