First, then, we have a prism which receives the light from the electric lamp, and which is called the polarizer.  Then we have the plate of gypsum (supposed to be placed at S, fig. 36), and then the prism in front, which is called the analyzer.  On its emergence from the first prism, the light is polarized; and, in the particular case now before us, its vibrations are executed in a horizontal plane.  We have to examine what occurs when the two directions of vibration in the interposed gypsum are oblique to the horizon.  Draw a rectangular cross (A B, C D, fig. 37) to represent these two directions.  Draw a line (a b) to represent the amplitude of the horizontal vibration on the emergence of the light from the first Nicol.  Let fall from each end of this line two perpendiculars (a c, a f, b d, b e) on the two arms of the cross; then the distances (c d, e f) between the feet of these perpendiculars represent the amplitudes of two rectangular vibrations, which are the components of the first single vibration.  Thus the polarized ray, when it enters the gypsum, is resolved into its two equivalents, which vibrate at right angles to each other.

[Illustration; Fig. 37.]

In one of these two rectangular directions the ether within the gypsum is more sluggish than in the other; and, as a consequence, the waves that follow this direction are more retarded than the others.  In both cases the undulations are shortened when they enter the gypsum, but in the one case they are more shortened than in the other.  You can readily imagine that in this way the one system of waves may get half a wave-length, or indeed any number of half wavelengths, in advance of the other.  The possibility of interference here at once flashes upon the mind.  A little consideration, however, will render it evident that, as long as the vibrations are executed at right angles to each other, they cannot quench each other, no matter what the retardation may be.  This brings us at once to the part played by the analyzer.  Its sole function is to recompound the two vibrations emergent from the gypsum.  It reduces them to a single plane, where, if one of them be retarded by the proper amount, extinction will occur.

But here, as in the case of thin films, the different lengths of the waves of light come into play.  Red will require a greater thickness to produce the retardation necessary for extinction than blue; consequently when the longer waves have been withdrawn by interference, the shorter ones remain, the film of gypsum shining with the colours which the short waves confer.  Conversely, when the shorter waves have been withdrawn, the thickness is such that the longer waves remain.  An elementary consideration suffices to show, that when the directions of vibration of the prisms and the gypsum enclose an angle of forty-five degrees, the colours are at their maximum brilliancy.  When the film is turned from this direction, the colours gradually fade, until, at the point where the directions of vibration in plate and prisms are parallel, they disappear altogether.