Question

A filter for a camera contains 2 parallel plates of polarizing glass, one fixed and the other able to rotate. If (theta) is the angle of rotation from position of maximum light transmisison, then the intensity of light leaving the filter is cos^2(theta) times the intensity entering the filter. [equation given is I(cos^2(theta))=.4I ]

Find theta so that the light leaving the filter is 40% of that entering.

Answer 1

You could first argue that theta should be in the range \(0 \leq \theta \lt 90^\circ\) so that \(\cos(\theta)\) is positive.

Answer 2

Then by takes square roots on both sides you get \(\cos(\theta) = \sqrt{.4}\). Take arccos on both sides to get \(\theta = \arccos\sqrt{.4}\)

Answer 3

Which is about \(50.8^\circ\).

Answer 4

Thank you ^^

Answer 5

you're welcome :)