An electromagnetic wave passes through a sequence of three polarizers, which can be placed in any order. Polarizer A has its transmission axis vertical; polarizer B has its transmission axis horizontal; and polarizer C has its transmission axis at 10° to the vertical.

If the incident wave is unpolarized, in what order should you place the polarizers to maximize the intensity of the wave emerging from the last polarizer in the sequence?

1. Polarizer A, then C, then B
2. Polarizer B, then C, then A
3. Either of the above, they’d give the same final intensity
4. Polarizer C, then A, then B
5. Polarizer C, then B, then A
6. It doesn’t matter what order they’re in, none of the wave gets through

C must be between A and B, or else all of the wave would be absorbed. Choice 3 is correct, A-C-B or B-C-A. In both cases the transmitted intensity is:
I = I_o * 0.5 * cos²10 cos²80

If the incident wave is linearly polarized with its polarization direction at 10° to the vertical (parallel with polarizer C), in what order should you place the polarizers to maximize the intensity of the wave emerging from the last polarizer in the sequence?

1. Polarizer A, then C, then B
2. Polarizer B, then C, then A
3. Either of the above, they’d give the same final intensity
4. Polarizer C, then A, then B
5. Polarizer C, then B, then A
6. It doesn’t matter what order they’re in, none of the wave gets through

Again C must be between A and B, or else all of the wave would be absorbed. To maximize the intensity the order should be A-C-B. That gives a final intensity of:
I = I_o cos²10 cos²10 cos²80

That's larger than B-C-A, I = I_o cos²80 cos²80 cos²10