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

5. Summary

The theory of the diffraction of light by sound waves of high frequency developed in our earlier paper is extended to the case when the light beam is incident at an angle to the sound wave-fronts, both from a geometrical point of view and an analytical one. It is found that the maxima of intensity of the diffracted light occur in directions which make definite angles, denoted byϑ, with the direction of the incident light given by

$$\sin (\theta + \phi ) - sin \phi = \pm {{n\lambda } \over {\lambda * }}, n (an integer) \ge 0$$

whereλ andλ* are the wave-lengths of the incident light and the sound waves in the medium. The relative intensity of themth order to thenth order is given by

$$J_m ^2 \left( {v_0 \sec \phi {{\sin t} \over t}} \right) / J_n ^2 \left( {v_0 \sec \phi {{\sin t} \over t}} \right) $$

wherev ₀=2πµL /λ,t=πL tanφ /λ*,φ is the inclination of the incident beam of light to the sound waves,μ is the maximum variation of the refractive index in the medium when the sound waves are present and L secφ is the distance of the light path in the medium. These results explain the variations of the intensity among the various orders noticed by Debye and Sears for variations ofφ in a very gratifying manner.