Question

A mark on the surface of a glass sphere($\mu =$1.5) is viewed from a diametrically opposite position. It appears to be at a distance 10 cm from its actual position. The radius of sphere is:

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 20 cm

Answer 1

The correct option is A 5 cm

We write the formula for refraction through a spherical surface.

As we know

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

Here $v=10-2R,u=2R$

$\frac{1}{10-2R}-\frac{1.5}{-2R}=\frac{1-1.5}{-R}$

Solving this equation for the value of $R,$
we get,
$R=-5cm$

Therefore the radius of the sphere is $5cm.$