In the adjacent diagram, CP represents a wave | vedclass

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Question

(b)$PR = d ==> PO = d sec 	heta$ and $CO = PO\, cos\, 2 	heta = d \,sec 	heta \cos 2 	heta $ is

Path difference between the two rays
$\Delt

Vedclass · Accepted Answer

$cos 	heta = \lambda /4d$

Vedclass · Answer

(b)$PR = d ==> PO = d sec 	heta$ and $CO = PO\, cos\, 2 	heta = d \,sec 	heta \cos 2 	heta $ is

Path difference between the two rays
$\Delta = CO + PO = (d \,sec 	heta  + d\, sec\, 	heta \,cos\, 2 	heta )$
Phase difference between the two rays is
$\phi = \pi$ (One is reflected, while another is direct)
Therefore condition for constructive interference should be $\Delta = \frac{\lambda }{2},\frac{{3\lambda }}{2}......$
or $d\sec 	heta (1 + \cos 2	heta ) = \frac{\lambda }{2}$
or $\frac{d}{{\cos 	heta }}(2{\cos ^2}	heta ) = \frac{\lambda }{2}$ ==> $\cos 	heta = \frac{\lambda }{{4d}}$

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

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