posted by michael .
Two sheets of polaroid are arranged with their polarisation axes at angles of 0 and
90 degrees relative to the horizontal. Randomly polarized light is shone so that it
passes through both filters. What fraction of the light is transmitted?
A further, third sheet of polaroid is now introduced between them with its polarisation
axis at an angle θ to the horizontal. What fraction of the original light intensity now
passes through this arrangement?
What is the maximum possible transmitted fraction?
The answer to part 1 is zero.
Sheet Polaroid has inherent losses of about 50%, even for the favored plane of polarization. Therefore I have no further comment about part 2 of your question. Their answer will be wrong. Some light will get through because the polarizer in the middle repolarizes the light.