Calculating Polarization Intensity: Theta Values of 45 and 25 Degrees Explained

[lozah]

Homework Statement

Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two such that its transmission axis makes an angle θ with that of the first sheet. Unpolarized light of intensity I0 is incident on the first sheet. Find the intensity of the light transmitted through all three sheets for the following values of θ.

The two values of theta are 45 and 25 degrees.

Homework Equations

I(transmitted)=I(incident)*(cos(theta))^2

The Attempt at a Solution

I got all of the answers right for theta = 45 degrees. Through the first polarizer, it was 0.5, then 0.25, then 0.125, but I can't seem to get the answer right for theta = 25 when it's gone through all of the polarizers.

The first two I got like this:
I1 = I0 * 0.5
I2 = (I0*0.5)(cos25)^2 = 0.411 * I0
I3 = (I0*0.411)(cos25)^2 = 0.337 * I0

But my answer for I3 is wrong. Can anyone help me? Thanks.

 

[TSny]

I1 = I0 * 0.5
I2 = (I0*0.5)(cos25)^2 = 0.411 * I0
I3 = (I0*0.411)(cos25)^2 = 0.337 * I0

But my answer for I3 is wrong. Can anyone help me? Thanks.

The 25 degrees for I3 is not correct. Can you see why?

 

[lozah]

The 25 degrees for I3 is not correct. Can you see why?

Yup I just got it right before I got the notification that you replied! It should be 65 degrees because that is the change in angle from 25 degrees to 90 degrees (in order to accommodate the fact that the outer two polarizers have their transmission axes crossed). THANKS!

 

[TSny]

OK, Good!