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
Show Answer
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} $
