15. "In class, you showed us that if you put another polarizer between two sheets of polarizer which are at 90o to each other, light is transmitted. You had the angle between the first and second polarizer as 45o. Does it work at other angles?"
The arrangement you are referring to is shown below, with the angle between polarizer 1 and polarizer 3 set at 90o.
Let the angle between polarizer 2 - the one we can rotate - and #1 be A. We can work out what the transmitted intensity is from #3 as a function of angle A, using Malus' Law. If Io is the intensity of the incoming, unpolarized light to #1, the intensity transmitted by #1, i.e., the intensity falling on #2, is Io/2. By Malus' Law, the intensity transmitted by #2 is:
and this falls on #3. Again, using Malus' Law, and noting that the angle between #2 and #3 is (90 - A), the intensity transmitted by #3 is:
A plot of this intensity is shown below.
You'll notice that the only values of A where there is zero transmitted intensity are, 0, 90o, 180o, etc., i.e., when the polarization direction of #2 is parallel to either #1 or #3. The transmitted intensity is a maximum 45o away from the zero intensity positions ... and that's why I chose the 45o angle for the in-class problem.
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