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

Question

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

Dr. Abubacker · Accepted Answer

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

Q. 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 $OP$

Explanation

Reviewed by Dr. Abubacker

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