Comparison of Wave-lengths with a Fabry and Perot Étalon

Abstract

IN investigations on the accurate measurement of wave-lengths by means of a Fabry and Perot étalon, it is possible to obtain the desired values without the necessity of measuring the focal length of the optical system. In such work as carried on by Rayleigh (Phil. Mag. 11, 685, 1906), Fabry and Perot (Astrophys. Jour. 15, 73, 1902), Eversheim (Astrophys. Jour. 26, 172, 1907), Pfund (Astrophys. Jour. 28, 197, 1908), Brown (Astrophys. Jour. 56, 53, 1922), and others, use is made of the relation. where y, y′ are the two wave-lengths to be compared; x and x′ are angular diameters of the first rings; and p and p′ are the corresponding orders of interference. The problem may be simplified, however, by a variation in the method which requires a measurement of only linear diameters. In the simpler method the above expression is replaced by the more fundamental one, from which indeed it is derived: where a is the fractional part of the number which gives the order of interference for wave-length y, corresponding to the centre of the ring system. Now the value of a, (and a′) may readily be obtained from measurements of linear diameters by making use of the relation where dk and dnare linear diameters of the kth and the nth rings. This expression, which is a generalised form of one used by Merton (Proc. Roy. Soc. A, 96, 388, 1920) in an investigation on the spectra of isotopes, may be deduced easily from the fundamental equation of the etalon (path difference = 2t cos xn). The accompanying table, in which numbers are calculated from measurements of a plate taken by one of the writer's students, gives an idea of the accuracy of the method.