 Solution

On rotating a fixed crystallite around the microscope axis, the angle $\alpha$ to the fixed polarizer changes. The factor ${\sin }^2(2\alpha )$ repeats every90degrees. Each birefringent region is therefore extinguished four times in a complete revolution and reaches maximum brightness45degrees from its own extinction positions.

Different regions need not extinguish together if their principal in-plane directions differ. For a fixed propagation direction through a uniform region, azimuthal rotation changes brightness more directly than its retardation colour: the underlying index difference and thickness remain the same. The isotropic unstressed matrix remains dark throughout rotation.