The answers to othese questions can be obtained by multiplying the matrices involved. For light to pass there must be non-zero elements in the product (final) matrix. If the matrix is the same as either of the spin states or the combination states, the nature of the light is identified. If the product matrix is non-zero but different from any of the up-down or plus-minus states, the light passing through the system is some combination of the above. The answers are given below along with a photograph of each series of cubes being used:
Part 1.
Please notice that the question was not what optical element is actually in the sigma cubes!
Part 2. The answer is (e): a sheet of clear plastic that does nothing optically. As far as I can tell, the "identity" matrix optical cube does nothing optically. This would be analogous to the identity matrix itself: when you multiply any matrix by the identity matrix you get the same matrix.
