CBSE 2025, Set 2

Question

A ray of light is incident at an angle $i$ on a parallel sided glass slab of thickness '$d$' and gets refracted into the slab at angle $r$. Draw a ray diagram to show its path as its emerges out of the slab. Hence, obtain an expression for the lateral shift of the ray. Under what condition will the shift be minimum?

Edvaya · Accepted Answer

The correct answer is Subjective. **Ray Diagram:**

![Lateral Shift Ray Diagram](https://www.edvaya.com/images/cbse/physics/2025/set2/q24-lateral-shift-glass-slab-answer.webp)

**Expression for Lateral Shift:**
Let the lateral shift be $CD$ (the perpendicular distance between the incident ray extended and the emergent ray). 
Let the thickness of the slab be $d = BE$.
In the right-angled triangle $\Delta BCD$, the angle $\angle DBC = i - r$:
$$\sin(i - r) = \frac{CD}{BC} \quad 	ext{--- (1)}$$

In the right-angled triangle $\Delta BCE$, the angle $\angle CBE = r$:
$$\cos r = \frac{BE}{BC} = \frac{d}{BC}$$
$$BC = \frac{d}{\cos r}$$

Substitute the value of $BC$ into equation (1):
$$CD = BC \sin(i - r)$$
$$\boxed{	ext{Lateral Shift } (CD) = \frac{d \sin(i - r)}{\cos r}}$$

**Condition for Minimum Shift:**
The shift will be minimum (zero) when the angle of incidence $i$ is minimum (i.e., normal incidence, $i = 0^\circ$). When $i = 0$, $r = 0$, so $\sin(0) = 0$, leading to zero lateral shift.

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Physics > Optics > Ray Optics And Optical Instruments

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