Question

An object O is stuck on the surface of a transparent solid sphere of radius 20 cm. The refractive index of the sphere such that rays from the object after refraction from the opposite side emerge as a parallel beam is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $1.5$
• D. $2$

Answer 1

The correct option is D $2$

As the rays coming out from other surface are parallel therefore, distance of image from refracting surface (other surface) will be:

$v=\infty$

The object is stuck on one surface of transparent solid, therefore distance of object fromurefracting surface (other surface) will be:

$u=diameter=40cm$

This is the case of refraction from concave surface (when object lies in denser medium ) for which it is given that

$v=\infty ,u=-40cm,R=-20cm$

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

where ${\mu }_1=$ refractive index of sphere

${\mu }_2=1$ , refractive index of air

$\frac{1}{\infty }-\frac{{\mu }_1}{-40}=\frac{1-{\mu }_1}{-20}$

$\frac{{\mu }_1}{40}=\frac{1-{\mu }_1}{-20}$

${\mu }_1=2$