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

Doppler effect and coherence phenomena

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## Summary

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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## References

1. C. V. Raman and N. S. Nagendra Nath,Proc. Ind.Acad. Sci. (A), 1935,2, 406.

2. C. V. Raman and N. S. Nagendra Nath.Proc. Ind. Acad. Sci. (A). 1935,2, 413.

3. R. Bar,Helv. Phy. Acta, 1933,6, 570.

4. P. Dcbye and F. W. Sears,Proc. Nat. Acad. Sci. (Washington), 1932,18, 409.

5. R. Bar,Helv. Phy. Acta, 1933,8, 591.

6. “A Treatise on the Theory of Bessel Functions” by G. N. Watson. 1922, p. 359.

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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). https://doi.org/10.1007/BF03046238