Question

In the figure shown, a point object $O$ is placed in air. A spherical boundary of radius of curvature $1.0m$ separates two media. $AB$ is the principal axis. The refractive index above $AB$ is $1.6$ and below $AB$ is $\mathrm{2.0.}$ The separation between the images formed due to refraction at the spherical surface is

• A. $12m$
• B. $20m$
• C. $14m$
• D. $10m$

Answer 1

The correct option is A $12m$

Consider the following ray diagram


Two separate images are formed due to refraction through regions 1 and 2. Using the Gaussian formula for curved surface, we can find the image distance in both cases

For region 1,

$\frac{{\mu }_2}{v}-\frac{m{u}_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1.6}{v}+\frac{1}{2}=\frac{1.6-1}{1}$
$\Rightarrow v=16m$

For region 2,

$\frac{{\mu }_2}{v}-\frac{m{u}_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{2}{v}+\frac{1}{2}=\frac{2}{1}$
$\Rightarrow v=4m$


Therefore, separation between images $=16-4=12m$