Question

A beam of diameter $d$ is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to $d$ , then the diameter of the beam at the base of the hemisphere will be

• A. $\frac{3}{4}d$
• B. $d$
• C. $\frac{d}{3}$
• D. $\frac{2}{3}d$

Answer 1

Answer: (D)

$\frac{\mu _{2}}{\text{v}} - \frac{\mu _{1}}{\text{u}} = \frac{\mu _{2} - \mu _{1}}{\text{R}} \Rightarrow \frac{3}{2 \text{v}} - \frac{1}{\infty } = \frac{\frac{3}{2} - 1}{\text{R}} \Rightarrow \frac{3}{2 \text{v}} = \frac{1}{2 \text{R}}$
$\text{v} = 3 \text{R} \Rightarrow \frac{\text{d}}{3 \text{R}} = \frac{\text{d}^{'}}{2 \text{R}} \Rightarrow \text{d}^{'} = \frac{2}{3} \text{d}$