 Solution

For two-element polarization identification, assume ideal elements and use an intensity detector. For each source, test both element orders while rotating their relative axes. The circular source followed by the quarter-wave plate and then the polarizer is the combination that gives full intensity modulation. The plate converts circular light to linear light, and the downstream polarizer then obeys Malus's law.

If the polarizer comes first, it transmits half the circular source's intensity and the downstream lossless plate cannot change that intensity. Unpolarized light also gives constant half-intensity in either order: a wave plate leaves it unpolarized, while a polarizer followed by a wave plate has no final analyzer. Thus the modulating source is circular, its first element is the quarter-wave plate, and its second is the polarizer; the remaining source is unpolarized. Testing both orders avoids needing to know either source's original brightness.