Understanding Polarization: Solving a Problem with the Law of Malus

[muirontriton]

Hello,
I was wondering if any of you guys can tell me whether or not I did the following polarization problem correct.

Problem:
Polarized light passes through a sequence of two polarizers whose axis of polarization forms a 30 degree angle. The second polarizer has the same polarization as the incoming light before it hits the first polarizer. What fraction if the incident intensity emerges from the set of polarizers?

The answer is 1/2.

My attempt:
I used the Law of Malus:
S = S(i)*cos^2(θ)

So I did this:

cos^3(30) * cos^2(30) * S(i) = S

The cos^3(30) comes from the average of the first two polarizers. As for the second part, I am not sure. I assumed that the problem says the angle is still 30° after the light goes through the first two. In the end, I get .49, which is close to the answer. However, I feel strongly that what I did is completely wrong. Is this correct?

 

[harts]

That cos^3 is what is messing you up.

You know that the first polarizer brings it down to a fraction of .75.

Now how can you bring it down another 2/3?

I honestly don't know myself - there are no even angles that when put into cos^2 equal 2/3. I could be horribly wrong, but are you sure the answer is 1/2?

 

[muirontriton]

The answer is still 1/2.

What does it mean by "the second polarizer has the same polarization as the incoming light before it hits the first polarizer?"

 

[harts]

http://lectureonline.cl.msu.edu/~mmp/kap24/polarizers/Polarizer.htm

Look at this applet. Change it to the two polarizer setting. Rotate the first polarizer 30 degrees (so 60 or 120 degrees, doesn't matter which). As far as I can tell, this is the situation described. That's why I'm confused. It's not 1/2. Maybe I'm wrong.

To answer your question, I'm pretty confident that that means it is at the same angle as the incoming light.

 

[muirontriton]

But this is with a beam of unpolarized light entering the polarizers. The light entering the polarizers is polarized. I used the applet and set the two polarizers to 30 degrees, and I got an intensity of 50%. That would make sense, but the light coming in is polarized, so wouldn't that lead a different approach?