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Question

(C) The path difference between the beams reflected from two successive planes is given by $\Delta x = 2d \sin 	heta$,where $	heta$ is the glancing

Vedclass · Accepted Answer

$\sin^{-1}\left(\frac{n\lambda}{2d}\right)$

Vedclass · Answer

(C) The path difference between the beams reflected from two successive planes is given by $\Delta x = 2d \sin 	heta$,where $	heta$ is the glancing angle (the angle between the incident beam and the plane).For constructive interference,the path difference must be an integer multiple of the wavelength:$\Delta x = n\lambda$Substituting the expression for path difference:$2d \sin 	heta = n\lambda$$\sin 	heta = \frac{n\lambda}{2d}$$	heta = \sin^{-1}\left(\frac{n\lambda}{2d}ight)$Thus,the correct option is $C$.

$A$ beam with wavelength $\lambda$ falls on a stack of partially reflecting planes with separation $d$. The angle $\theta$ that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where $n = 1, 2, \dots$)

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