JEE Physics 2025 Question with Solution

Given: A parallel-sided glass slab of thickness $h$ is placed in air. A ray is incident at angle $i$ and refracts inside the slab at angle $r$.

Find: The lateral shift of the emergent ray.

Concept: In a parallel-sided slab, the ray emerges parallel to the incident ray but gets displaced sideways. This sideways displacement is called the lateral shift.

From the geometry of refraction in the slab, the lateral shift is

$$S = \frac{h \sin(i-r)}{\cos r}$$

where $h$ is the slab thickness, $i$ is the angle of incidence, and $r$ is the angle of refraction.

Therefore, the correct formula for the lateral shift is

$$\frac{h \sin(i-r)}{\cos r}$$

So, the correct option is D.

Given: Thickness of slab $h$, angle of incidence $i$, and angle of refraction $r$.

Find: Lateral shift $d$.

Inside the slab, the ray travels along a slanted path. If the refracted path length inside the slab is $L$, then from geometry

$$L = h \sec r$$

The lateral shift is the component of this path associated with the angle difference $i-r$. Hence,

$$d = L \sin(i-r)$$

Substituting $L = h \sec r$,

$$d = h \sec r \cdot \sin(i-r)$$

Using $\sec r = \frac{1}{\cos r}$,

$$d = \frac{h \sin(i-r)}{\cos r}$$

Thus, the lateral shift is $\frac{h \sin(i-r)}{\cos r}$, so the correct option is D.