Question

In the adjacent, $CP$ 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 $OP$.

• A. $\cos \theta =3\lambda /2d$
• B. $\cos \theta =\lambda /4d$
• C. $\sec \theta -\cos \theta =\lambda d$
• D. $\sec \theta -\cos \theta =4\lambda d$

Answer 1

The correct option is B $\cos \theta =\lambda /4d$

For constructive interference

$\Delta \varphi =(d\sec \theta +d\sec \theta \cos 2\theta )\frac{2\pi }{\lambda }+\pi =2n\pi$

$\Rightarrow \cos \theta =\frac{(2n-1)\lambda }{4d}$

Hence $\left(B\right)$ is correct.