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(D) For constructive interference,the path difference between waves reflected from successive atomic planes must be an integral multiple of the wavele

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$2 d \cos i = n \lambda_{dB}$

Vedclass · Answer

(D) For constructive interference,the path difference between waves reflected from successive atomic planes must be an integral multiple of the wavelength,which is given by Bragg's Law: $2d \sin 	heta = n \lambda_{dB}$,where $	heta$ is the glancing angle (the angle between the incident ray and the crystal plane).From the provided figure,the angle $i$ is the angle between the incident ray and the normal to the crystal plane. Therefore,the glancing angle $	heta$ is given by $	heta = 90^{\circ} - i$.Substituting this into Bragg's Law:$2d \sin(90^{\circ} - i) = n \lambda_{dB}$Since $\sin(90^{\circ} - i) = \cos i$,we get:$2d \cos i = n \lambda_{dB}$

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