Optics Question 137

Question: In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP

[IIT-JEE (Screening) 2003]

Options:

A) cosq = 3l/2d

B) cosq = l/4d

C) secq ? cosq = l/d

D) secq ? cosq = 4l/d

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Answer:

Correct Answer: B

Solution:

$ \because $ PR = d

Therefore PO = d secq and CO = PO cos 2q $ =d\sec \theta \cos 2\theta $ is Path difference between the two rays D = CO + PO = (d secq + d secq cos 2q)

Phase difference between the two rays is f = p (One is reflected, while another is direct)

Therefore condition for constructive interference should be $ \Delta =\frac{\lambda }{2},\frac{3\lambda }{2}…… $ or $ d\sec \theta (1+\cos 2\theta )=\frac{\lambda }{2} $ or $ \frac{d}{\cos \theta }(2{{\cos }^{2}}\theta )=\frac{\lambda }{2} $

Therefore $ \cos \theta =\frac{\lambda }{4d} $



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