Why Does Unpolarized Light Lose Half Its Intensity Through a Polaroid?

[superslow991]

Homework Statement

Unpolarized light of intensity Io passed through a Polaroid sheet with its polarizing axis at the 12 o'clock position and then through a second with its polarizing axis at the 1 o'clock position. What is the intensity of the emerging light?

Homework Equations

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I= I0 *0.5*cos2(30)

The Attempt at a Solution

Now i know the solution i just want a break down of the question. Why is it that when a unpolarized light passed through a polaroid, it loses 1/2 its intensity?

Also where would the 30 degrees come from? Also is it possible to draw this question out?

 

[FactChecker]

Intuitively, the factor of 0.5 is because the unpolarized light is exactly as likely to have components aligned with the filter direction as at right angles. So half the light intensity gets through. You can probably do a little trig and calculus to calculate the 0.5. The cos(30) is due to the angle between the first filter at 12 o'clock and the second filter at 1 o'clock.

 

[superslow991]

Intuitively, the factor of 0.5 is because the unpolarized light is exactly as likely to have components aligned with the filter direction as at right angles. So half the light intensity gets through. You can probably do a little trig and calculus to calculate the 0.5. The cos(30) is due to the angle between the first filter at 12 o'clock and the second filter at 1 o'clock.

Hmm how can you be sure that the angle between the 12 o clock filter and 1 o clock filter is 30 degrees though?

 

[FactChecker]

Hmm how can you be sure that the angle between the 12 o clock filter and 1 o clock filter is 30 degrees though?

12 o'clock is straight up and 3 o'clock is horizontal so that is 90°. So 1 o'clock is 1/3 * 90° = 30°

 

[superslow991]

12 o'clock is straight up and 3 o'clock is horizontal so that is 90°. So 1 o'clock is 1/3 * 90° = 30°

ok thanks a lot