Angle between polarizer and analyzer

[bobsmithe]

Homework Statement

Consider a polarizer-analyzer arrangement, as shown (here's a link http://i.imgur.com/APZRJ6J.png )

At what angle is the axis of the analyzer to the axis of the polarizer if, after passing through both sheets, the beam intensity is reduced by 67.6 percent?
Answer in units of ◦

Homework Equations

I=(1/2)I_o
I=I_o*cos^2(∅)

The Attempt at a Solution

Since the beam intensity is reduced by 67.7%, I knew I/I_o was .676, so I tried doing ∅=cos($\sqrt{.676}$) but it wasn't right. I'm not sure what I did wrong and whether I'm supposed to use the first equation in this type of problem or not.

 

[BOYLANATOR]

It wasn't reduced to 67.6 percent. It was reduced by 67.6 percent

 

[bobsmithe]

so that would mean that .324I=I_o*cos^2(∅)?

 

[bobsmithe]

ok I got it. Thanks for pointing out my mistake

 

[Nickie]

I would like to clarify that the angle between the polarizer and the analyzer is not related to the reduction in beam intensity. The angle between the polarizer and the analyzer determines the amount of polarized light that can pass through the two sheets.

To find the angle between the polarizer and the analyzer, we can use the second equation given in the homework, where I_o is the initial intensity and I is the intensity after passing through both sheets. We can set I/I_o equal to 0.676 and solve for ∅.

0.676 = cos^2(∅)

Taking the square root of both sides, we get:

0.822 = cos(∅)

Using a calculator, we can find that the angle between the polarizer and the analyzer is 34.2°. This means that the axis of the analyzer is at an angle of 34.2° to the axis of the polarizer.

I hope this helps!