Question

A mark placed on the surface of a sphere is viewed through glass from a position directly opposite as shown in the figure. The diameter of the sphere is $30cm$ and refractive index of glass is $1.5$. The position of the image is

• A. at a distance of $60cm$ from surface $ABC$ in the direction of incident light
• B. at a distance of $60cm$ from the surface $ABC$ opposite to the direction of incident light
• C. at a distance of $30cm$ from the surface $AOC$ opposite to the direction of incident light on $ABC$
• D. Both (b) and (c)

Answer 1

Answer: (B)

Given, for refraction at spherical surface $ABC$,

$u=2R=-30cm$
${\mu }_1=1.5$
$\Rightarrow {\mu }_2=1.0$
$v=?$
Applying, $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1}{v}-\frac{1.5}{(-30)}=\frac{(1-1.5)}{(-15)}$
$\Rightarrow \frac{1}{v}+\frac{1.5}{30}=\frac{-0.5}{-15}$
$\Rightarrow \frac{1}{v}=\frac{0.5}{15}-\frac{1.5}{30}$
$\Rightarrow v=-60cm$
The image is at a distance of $60cm$ from surface $ABC$ opposite to the direction of incident light.