Question

A clear transparent glass sphere $(\mu=1.5)$ of radius $R$ is immersed in a liquid of refractive index $1.25$. A parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

• A. $-3 R$
• B. $+3 R$
• C. $-R$
• D. $+R$

Answer 1

Answer: (B)

$\frac{\mu_{1}}{-u}+\frac{\mu_{2}}{v}=\frac{\mu_{2}-\mu_{1}}{R}$
$ \frac{1.25}{-(-\infty)}+\frac{1.5}{v}=\frac{1.5-1.25}{R}$
or $\frac{1.5}{v}=\frac{0.25}{R}$
or $ v=\frac{1.5 R}{0.25}=6 R$

Again, $\frac{\mu_{2}}{-u}+\frac{\mu_{1}}{v}=\frac{\mu_{1}-\mu_{2}}{R}$
$\frac{1.5}{-4 R}+\frac{12.5}{v}=\frac{1.25-1.5}{-R}$
or $ \frac{1.25}{v}=\frac{1}{4 R}+\frac{1.5}{4 R}=\frac{2.5}{4 R}$
$=\frac{1.25 \times 4 R}{2.5}=\frac{5 R}{2.5}$ or $v=2 R$.
Distance from the center $=3 R$