Question

A glass sphere of radius $2R$ and refractive index $n$ has a spherical cavity of radius $R$, concentric with it.
When viewer is on right side of the follow sphere, what will be the apparent change in position of the object?

• A. $\frac{(n-1)}{(3n+1)}R$, toward left
• B. $\frac{(n+1)}{(3n-1)}R$, toward left
• C. $\frac{(n+1)}{(3n+1)}R$, toward right
• D. $\frac{(n-1)}{(3n-1)}R$, toward right

Answer 1

The correct option is D $\frac{(n-1)}{(3n-1)}R$, toward right

Considering refraction at surface 3,

$\frac{n}{v}-\frac{1}{-2R}=\frac{n-1}{-R}$

Therefore, $v=\frac{2nR}{1-2n}$

This image acts as an object for refraction from surface 4.

Considering refraction at surface 4,

$u=\frac{2nR}{1-2n}-R=\frac{(4n-1)R}{1-2n}$

$\frac{1}{v}-\frac{n}{\frac{(4n-1)R}{1-2n}}=\frac{1-n}{-2R}$

Therefore $v=\frac{2(4n-1)R}{1-3n}$

Thus the apparent change in the position of object= Distance between object

and the final image=$\frac{2(4n-1)R}{1-3n}+3R=\frac{(n-1)R}{3n-1}$

Since this value is positive, the change is towards right.