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