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

Answer 1

The correct option is B $+3R$

$\frac{{\mu }_1}{-u}+\frac{{\mu }_2}{v}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1.25}{-(-\infty )}+\frac{1.5}{v}=\frac{1.5-1.25}{R}$ or $\frac{1.5}{v}=\frac{0.25}{R}$
or $v=\frac{1.5R}{0.25}=6R$
Again, $\frac{{\mu }_2}{-u}+\frac{{\mu }_1}{v}=\frac{{\mu }_1-{\mu }_2}{R}$
$\frac{1.5}{-4R}+\frac{12.5}{v}=\frac{1.25-1.5}{-R}$
or $\frac{1.25}{v}=\frac{1}{4R}+\frac{1.5}{4R}=\frac{2.5}{4R}$
or $=\frac{1.25\times 4R}{2.5}=\frac{5R}{2.5}$
or $v=2R$.
Distance from the center $=3R$.