The phenomenon of interference produced by crystalline plates is considerably modified if the light be circularly or elliptically polarized or analysed by the interposition of a quarter-wave between the crystal and the polarizer or analyser.
Conversely a quarter-wave plate may be employed for reducing a circularly or elliptically polarized stream to a state of plane polarization.
Wernicke and others have established that in general light polarized in any but the principal azimuths becomes elliptically polarized by reflection, the relative retardation of phase of the components polarized in these azimuths becoming 42 at a certain angle of incidence, called the principal incidence.
Airy extended Fresnel's hypothesis to directions inclined to the axis of uniaxal crystals by assuming that in any such direction the two waves, that can be propagated without alteration of their state of polarization, are oppositely elliptically polarized with their planes of maximum polarization parallel and perpendicular to the principal plane of the wave, these becoming practically plane polarized at a small inclination to the optic axis.
They may be differentiated by first passing the light through a quarter-wave plate with its axis parallel or perpendicular to the plane of maximum polarization: for elliptically polarized light thereby becomes plane polarized and one of the streams is extinguished on rotating the rhomb; but with the other two kinds of light this is not the case, and the light is partially plane or partially elliptically polarized according as the plane of maximum polarization remains the same or is changed.
Elliptically polarized, partially elliptically polarized and partially plane polarized light give with Iceland spar two streams of, in general, unequal intensity, neither of which can be made to vanish.
In conformity with the form of the path, the light is said to be elliptically polarized, rightor left-handedly as the case may be, and the axes of the elliptic path are determined by the planes of maximum and minimum polarization of the light.