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The diffraction of light by high frequency sound waves: Part III

Doppler effect and coherence phenomena

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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. (1)

    In the case of the former the theory shows that the nth order which is inclined at an angle\(\sin ^{ - 1} \left( { - \begin{array}{*{20}c} {n\lambda } \\ {\lambda *} \\ \end{array} } \right)\) to the direction of the propagation of the incident light has the frequencyv – nv* wherev is the frequency of light,v* is the frequency of sound andn is a positive or negative integer and that thenth order has the relative intensity\(Jn^2 \left( {\frac{{2\pi \mu L}}{\lambda }} \right)\) 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 wave-length of light.

  2. (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 frequenciesv ± 2rv* wherer is an integer including zero, the relative intensity of thev ± 2rv* sub-component being\(J^2 n - r\left( {\frac{{\pi \mu L}}{\lambda }} \right)J^2 n + r\left( {\frac{{\pi \mu L}}{\lambda }} \right)\); any odd order, say 2n + 1, contains radiations with frequencies\(v \pm \overline {2r + 1} v*\), the relative intensity of the\(v \pm \overline {2r + 1} v*\) sub-component being\(J^2 n - r\left( {\frac{{\pi \mu L}}{\lambda }} \right)J^2 n + r + 1\left( {\frac{{\pi \mu L}}{\lambda }} \right)\). 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.

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Raman, C.V., Nagendra Nath, N.S. The diffraction of light by high frequency sound waves: Part III. Proc. Indian Acad. Sci. 3, 75–84 (1936).

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