Question

A point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is?

• A. $5$
• B. $5/3$
• C. $2$
• D. $2.5$

Answer 1

The correct option is C $2$

Given: A point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere.

To find the refractive index of the material of the sphere

Solution:

The distance of the source from the opposite surface of the sphere, $u=-2R$

Now,

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

where ${\mu }_2=1$ is the refractive index of the air

${\mu }_1=\mu$ is the refractive index of of the sphere.

and as the light emerges parallel, so the image is formed at infinity

$\therefore ,\frac{1}{\infty }-\frac{\mu }{-2R}=\frac{1-\mu }{-R}⟹\frac{\mu }{2R}=\frac{1-\mu }{-R}⟹-\mu =2-2\mu ⟹\mu =2$

is the required refractive index of the sphere.