Question

The angle of deviation produced by a thin prism when placed in air is $\delta_1$ and that when immersed in water is $\delta_2$. The refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. The ratio $\delta_1 : \delta_2$ is

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Hint:

Physics Tip : When a prism is immersed in a liquid, the relative refractive index decreases, which in turn reduces the angle of deviation.

Answer 1

The Correct Option is D

Concept: Physics (Optics) – Refraction through a Thin Prism.

Step 1: State the formula for deviation in a thin prism. For a thin prism, the angle of deviation is $\delta = (\mu - 1)A$, where $A$ is the prism angle.

Step 2: Calculate relative refractive indices.
• In air: $\mu_1 = \frac{\mu_{glass}}{\mu_{air}} = \frac{3/2}{1} = \frac{3}{2}$
• In water: $\mu_2 = \frac{\mu_{glass}}{\mu_{water}} = \frac{3/2}{4/3} = \frac{9}{8}$

Step 3: Find the ratio of deviations. $$\frac{\delta_1}{\delta_2} = \frac{\mu_1 - 1}{\mu_2 - 1}$$ $$\frac{\delta_1}{\delta_2} = \frac{\frac{3}{2} - 1}{\frac{9}{8} - 1} = \frac{1/2}{1/8} = \frac{8}{2} = 4$$ $$ \therefore \text{The ratio } \delta_{1}:\delta_{2} \text{ is } 4:1. $$