CLASSICAL THEORY OF LIGHT 755 



less-often is given by the first term on the right in equation (18), and 

 hence is greater by 180° than that between the second and the first; 

 and when i is so chosen that the second and the first are in opposite 

 phase, then all the beams of higher order are in the same phase as the 

 second and reinforce it, the reinforcement being just so great — in the 

 case of the transparent plate — that the resultant of all these beams 

 together is of the same amplitude as the first reflected beam. There- 

 fore the minima, the centres of the dark fringes, are not shifted by the 

 extra beams, but are rendered absolutely black. 



The width of the fringes is greater, the thinner the plate — -other 

 things, naturally, being left unchanged. This is the reason why one 

 needs quite a thin lamina of glass to see them well, and cannot get 

 them at all with a windowpane. If the thickness of the plate is 

 changing continually, one sees them narrowing or widening; one sees 

 also a phenomenon much more striking, the generation of rings one 

 after the other out of the centre of the fringe-system — if the plate is 

 growing thicker; the reverse, if it is shrinking. Glass plates capable 

 of shrinking or thickening at will are not as yet available; but at 

 times the former case is realized by a soap-bubble on the verge of 

 dissolution. Where the soap-film is about to give way, the fringes 

 rapidly dwindle and are swallowed up into the central spot of the 

 interference-system, which alternately turns dark and light, and finally 

 goes black just at the instant before the bubble bursts. From this final 

 blackness we infer that the value tt must be assigned to the constant 

 (Po of equation (3). Reflection from water to air and reflection from 

 air to water are accompanied by phase-changes differing from each 

 other by t, since the beams of light formed by two such reflections 

 destroy each other when the reflecting surfaces are immeasurably close. 

 But the bubble is too tender an instrument for practical use. The 

 plate of variable thickness must be a slab of empty space between 

 movable solid mirrors.* 



The interferometer of Fabry and Perot is precisely such a thing: 

 two half-silvered plates of glass facing each other across a narrow gap. 

 The like-named instrument of Michelson is the same in principle; 

 but by ingenious use of a third reflector, the two essential mirrors are 

 transposed far apart — a most valuable feature, as we shall see. The 

 incident wave-trains (coming from below, in Fig. 4) are divided by a 

 semi-transparent mirror C inclined at about 45° to their path, and 

 the fractions are sent off at right angles to one another, along the two 



* Or else Lummer's device of a pair of wedges so proportioned, that a face of one 

 may slide along a face of the other, while the two sides not in contact remain parallel 

 to one another. 



