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)

$\frac{{\mu }_2}{\text{v}}-\frac{{\mu }_1}{\text{u}}=\frac{{\mu }_2-{\mu }_1}{\text{R}}\Rightarrow \frac{3}{2\text{v}}-\frac{1}{\infty }=\frac{\frac{3}{2}-1}{\text{R}}\Rightarrow \frac{3}{2\text{v}}=\frac{1}{2\text{R}}$
$\text{v}=3\text{R}\Rightarrow \frac{\text{d}}{3\text{R}}=\frac{{\text{d}}^{{}^{\prime }}}{2\text{R}}\Rightarrow {\text{d}}^{{}^{\prime }}=\frac{2}{3}\text{d}$