Question

A plane wave of wavelength $\lambda$ is incident at an angle $\theta$ on a plane mirror. Maximum intensity will be observed at $P$, when

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

Answer 1

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

for max intensity

$CO+OP=$multiple of $\frac{\lambda }{2}$

from fig.

$\frac{dcos2\theta }{cos\theta }+\frac{d}{cos\theta }=\frac{\lambda }{2}\Rightarrow \frac{d(1+cos2\theta )}{\cos \theta }=\frac{\lambda }{2}\Rightarrow \frac{d2\cos {}^2\theta }{\cos \theta }=\frac{\lambda }{2}\Rightarrow \cos \theta =\frac{\lambda }{4d}$