A plane wave front of light is incident on a plane mirror as shown in…

The path difference between the disturbance reaching at point $P$ directly and after reflection (from the geometry of figure) $=d \sec \theta \cdot \cos 2 \theta+d \sec \theta+\frac{\lambda}{2}$;

Here $\frac{\lambda}{2}$ is due to the reflection from denser medium.

For maximum intensity

$d \sec \theta(1+\cos 2 \theta)+\frac{\lambda}{2}=n \lambda \quad \text { or } \quad \cos \theta=\frac{3 \lambda}{4 d}$

∴  (b)