Practicing Success
A plane wave front of light is incident on a plane mirror as shown in the figure. Intensity is maximum at P when |
$\cos \theta=\frac{\lambda}{2 d}$ $\cos \theta=\frac{3 \lambda}{4 d}$ $\sec \theta-\cos \theta=\frac{3 \lambda}{4 d}$ $\sec \theta-\cos \theta=\frac{\lambda}{2 d}$ |
$\cos \theta=\frac{3 \lambda}{4 d}$ |
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) |