= Solution
The <quartz compensator> is a <birefringent optical compensator>: a retarder of known principal directions. With its <principal axes> at45degrees to the <polarizer> and analyser, the previously dark isotropic background acquires the compensator's own <interference colour>. The crystals are now viewed through two retarders.
When a specimen's slow axis is parallel to the compensator's slow axis, the retardations add. A90degree relative principal-axis rotation pairs the specimen's slow axis with the compensator's fast axis, and the signed retardations subtract:
$$
\Gamma_{\rm total}=\Gamma_q+\Gamma_s
\quad\hbox{or}\quad
\Gamma_{\rm total}=\Gamma_q-\Gamma_s.
$$
Thus different crystallites can shift to higher or lower <interference> orders even if their original hue was similar. In the subtracting orientation, equal magnitudes can compensate and yield extinction. These shifts identify fast and slow specimen directions.
At a general relative angle the full <polarization> transformation is required; simple scalar addition is only valid for aligned <principal axes>. The source does not specify the compensator retardation, so no unique list of resulting named colours can be assigned. The robust predictions are a changed background, orientation-dependent addition or subtraction, and possible compensation.
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