Although light loses some intensity every time is passes through a polarizing fi

Question

Although light loses some intensity every time is passes through a polarizing filter, a longer series of filters can transmit more of a beam's intensity than a shorter series while rotating its polarization axis by the same angle. Demonstrate this by calculating the percentage of incident intensity transmitted through these two sets of filters:

1. A vertically polarized beam passes through two filters, tilted 30 degrees and 60 degrees from the vertical.

2. A vertically polarized beam passes through four tilter, tilted 15, 30, 45 and 60 degrees from the vertical.


Please help me understand by showing me step by step. I don't just want the answer I want to know how to do it. thanks in advance

Explanation / Answer

the fraction of intensity that passes through is given by (cos@)^2 where @ is the angle between the incident light and the axis of the polarizer.

In the first case the relevant angles are 30 and 30 (note: after passing through the first filter, the emerging light is oriented at 30 degrees... so the angle between the light and the next filter is 60-30 = 30 degrees also).

So the fraction that passes through both is (cos30)^2 * (cos30)^2 = 9/16 = 56.25%

In the same way, the second set of polarizers is

(cos15)^2*(cos15)^2 * (cos15)^2 * (cos15)^2 = 0.7578 = 75.78%

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