What is the principle of reversibility of light ? Show that the incident ray of light is parallel to the emergent ray of light when light falls obliquely on a side of a rectangular glass slab.

The Principle of Reversibility of Light states that if the path of a ray of light is reversed, it will exactly retrace its original path.

Proof for Parallelism of Incident and Emergent Rays:

Consider a rectangular glass slab $ABCD$. A ray of light $EO$ is incident on the air-glass interface at point $O$ with angle of incidence $i$.

1. At point $O$ (Air to Glass): By Snell's Law, $\frac{\sin i}{\sin r} = n_{21}$ (where $n_{21}$ is the refractive index of glass w.r.t. air).
2. At point $O'$ (Glass to Air): The ray is incident at angle $r$ (alternate interior angles) and emerges at angle $e$. By Snell's Law, $\frac{\sin r}{\sin e} = n_{12}$.
3. Since $n_{21} = \frac{1}{n_{12}}$, we have:

$$\frac{\sin i}{\sin r} = \frac{1}{\sin r / \sin e} = \frac{\sin e}{\sin r}$$

$$\sin i = \sin e \implies i = e$$

Since the angle of incidence equals the angle of emergence, the incident ray is parallel to the emergent ray, though it undergoes a lateral displacement.