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 left side of the hollow sphere, what will be the shift in position of the object?

• A. $\frac{(n+1)}{(n-1)}R$, right
• B. $\frac{(n-1)}{(n+1)}R$, right
• C. $\frac{(2n-1)}{(2n+1)}R$, left
• D. $\frac{2(n-1)}{(n+1)}R$, left

Answer 1

The correct option is B $\frac{(n-1)}{(n+1)}R$, right

Refraction occurs at surface 1 before the observer on the left sees the object O.

For that refraction, $u=+R$

Therefore,$\frac{1}{v_I}-\frac{n}{R}=\frac{1-n}{2R}$

$v_I=\frac{2R}{n+1}<R$

Thus the object looks as if shifted to left as seen by observer on the left by an amount of $R-\frac{2R}{n+1}=\frac{(n-1)R}{(n+1)}$