Question

A hemisphere of radius $R$, made of glass of refractive index $\left(3/2\right)$ is placed on the table. A point source of light is placed at a distance $2R$ from the centre of hemisphere. If source is viewed diametrically opposite side of hemisphere. Find the position of image of source.

• A. 5R
• B. 6R
• C. 7R
• D. 8R

Answer 1

The correct option is B 6R

Refraction due to first surface.

$\frac{\left(\frac{3}{2}\right)}{v_1}-\frac{1}{-R}=\frac{\frac{3}{2}-1}{R}\Rightarrow v_1=-3R$

Refraction due due second surface.

$\frac{1}{v}-\frac{3/2}{-(3R+2R)}=\frac{1-\frac{3}{2}}{-R}$

$\Rightarrow v=5R$

$\therefore$ Position of image from the centre of hemisphere is at a distance $6R$ opposite side of source.