The diffraction of light by high frequency sound waves. Part III. Doppler effect and coherence phenomena

Abstract

The theory developed in part I of this series of papers has been developed in this paper to find the Doppler effects in the diffraction components of light produced by the passage of light through a medium containing (1) a progressive supersonic wave and (2) a standing supersonic wave. (1) In the case of the former the theory shows that the nth order which is inclined at an angle sin-1 (-nλ/λ^∗) to the direction of the propagation of the incident light has the frequency ν-nν^∗ where ν is the frequency of light, ν^∗ is the frequency of sound and n is a positive or negative integer and that the nth order has the relative intensity J²_n(2πμL/λ) where μ is the maximum variation of the refractive index, L is the distance between the faces of the cell of incidence and emergence and λ is the wavelength of light. (2) In the case of a standing supersonic wave; the diffraction orders could be classed into two groups, one containing the even orders and the other odd orders; any even order, say 2n, contains radiations with frequencies ν±2rν^∗ where r is an integer including zero, the relative intensity of the ν±2rν^∗ sub-component being J²_n-r(πμL/λ) J²_n+r(πμL/λ); and odd order, say 2n+1, contains radiations with frequencies ν ± 2r+1̅ν^∗, the relative intensity of the ν ± 2r+1̅ν^∗ sub-component being J²_n-r , (πμL/λ) J²_n+r+1(πμL/λ). These results satisfactorily interpret the recent results of Bar that any two odd orders or even ones partly cohere while an odd one and an even one are incoherent.