How Does Changing the Angle of a Third Polarizer Affect Light Intensity?

[ObviousManiac]

Homework Statement

A helium-neon laser emits a beam of unpolarized light thatpasses through three Polaroid filters, as shown in the figure . The intensity of the laser beam is I_{o}.

Suppose the third filter were at an angle of 50˚, what would be the intensity at point C?

Homework Equations

I = Io cos^2(x)

I = Io/2 (Unpolarized light through transmission axis)

The Attempt at a Solution

I've tried a bunch of things...

First I calculated the intensity at point B, which I found to be .375 Io via (1/2)Io*cos^2(30˚)

Then I tried .375Io*cos^2(50˚)

and also tried replacing .375 with .375/2 and just 1/2

But I can't get my teacher's answer, which is .331 Io

 

[collinsmark]

First I calculated the intensity at point B, which I found to be .375 Io via (1/2)Io*cos^2(30˚)

So far so good!

Then I tried .375Io*cos^2(50˚)

But the light just passed through polarizer 2 which was configured at 30^o. That means not only the light is already polarized, but the light already has a polarization angle of 30^o before it even gets to polarizer 3 (the one configured at 50^o).

So what's the angular difference between polarizer 3's angle and the polarization angle of the light at B?

and also tried replacing .375 with .375/2 and just 1/2

Now you're just randomly guessing.