| 1 | = 1 + | (1 − e2)2 | ; |
| R | 4e2 sin2 (½κδ) |
from which we see that if e = 1 absolutely, 1/R = R = 1 for all values of δ. If e = 1 very nearly, R = 1 nearly for all values of δ for which sin2 (½κδ) is not very small. In the light reflected from an extended source, the ground will be of full brightness corresponding to the source, but it will be traversed by narrow dark lines. By transmitted light the ground, corresponding to general values of the obliquity, will be dark, but will be interrupted by narrow bright rings, whose position is determined by sin ½(κδ) = 0. In permitting for certain directions a complete transmission in spite of a high reflecting power (e) of the surfaces, the plate acts the part of a resonator.
There is no transparent material for which, unless at high obliquity, e approaches unity. In C. Fabry and A. Pérot’s apparatus the reflections at nearly perpendicular incidence are enhanced by lightly silvering the surfaces. In this way the advantage of narrowing the bright rings is attained in great measure without too heavy a sacrifice of light. The plate in the optical sense is one of air, and is bounded by plates of glass whose inner silvered surfaces are accurately flat and parallel. The outer surfaces need only ordinary flatness, and it is best that they be not quite parallel to the inner ones. The arrangement constitutes a spectroscope, inasmuch as it allows the structure of a complex spectrum line to be directly observed. If, for example, we look at a sodium flame, we see in general two distinct systems of narrow bright circles corresponding to the two D-lines. With particular values of the thickness of the plate of air the two systems may coincide so as to be seen as a single system, but a slight alteration of thickness will cause a separation.
It will be seen that in this apparatus the optical parts are themselves of extreme simplicity; but they require accuracy of construction and adjustment, and the demand in these respects is the more severe the further the ideal is pursued of narrowing the rings by increase of reflecting power. Two forms of mounting are employed. In one instrument, called the interferometer, the distance between the surfaces—the thickness of the plate—is adjustable over a wide range. In its complete development this instrument is elaborate and costly. The actual measurements of wave-lengths by Fabry and Pérot were for the most part effected by another form of instrument called an étalon or interference-gauge. The thickness of the optical plate is here fixed; the glasses are held up to metal knobs, acting as distance-pieces, by adjustable springs, and the final adjustment to parallelism is effected by regulating the pressure exerted by these springs. The distance between the surfaces may be 5 or 10 mm.
The theory of the comparison of wave-lengths by means of this apparatus is very simple, and it may be well to give it, following closely the statement of Fabry and Pérot (Ann. chim. phys., 1902, 25, p. 110). Consider first the cadmium radiation λ treated as a standard. It gives a system of rings. Let P be the ordinal number of one of these rings, for example the first counting from the centre. This integer is supposed known. The order of interference at the centre will be p = P + ε. We have to determine this number ε, lying ordinarily between 0 and 1. The diameter of the ring under consideration increases with ε; so that a measure of the diameter allows us to determine the latter. Let t be the thickness of the plate of air. The order of interference at the centre is p = 2t/λ. This corresponds to normal passage. At an obliquity i the order of interference is p cos i. Thus if x be the angular diameter of the ring P, p cos ½x = P; or since x is small,
p = P (1 + 1⁄8x2).
In like manner, from observations upon another radiation λ′ to be compared with λ, we have
p′ = P′ (1 + 1⁄8x′2);
whence if t be treated as an absolute constant,
| λ′ | = | P | ( 1 + | x2 | − | x′2 | ) |
| λ | P′ | 8 | 8 |