Question

Parallel rays (in air) are incident on a transparent sphere along its one diameter. After refraction, these rays converge at the other end of this diameter. The refractive index for the material of sphere is

• A. 1
• B. 1.5
• C. 1.6
• D. 2

Answer 1

The correct option is D 2

For refraction at spherical surface, using the formula,

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

where ${\mu }_2$ is the refractive index of the medium into which the light rays are entering

${\mu }_1$ is the refractive index of the medium from which the light rays are coming
$R$ is the radius of curvature of the spherical surface
$u$ and $v$ is the object distance and image distance respectively.

Given,

$u=\infty$

${\mu }_1=1$ (air)

Let $d$ be the diameter of the transparent sphere

$\Rightarrow v=d$

$\Rightarrow R=\frac{d}{2}$

Now, we have

$\frac{{\mu }_2}{d}-\frac{1}{\infty }=\frac{{\mu }_2-1}{(\frac{d}{2})}$

$\frac{{\mu }_2}{d}=2\frac{({\mu }_2-1)}{d}$

${\mu }_2=2{\mu }_2-2$

$\Rightarrow {\mu }_2=2$

Hence, the correct answer is OPTION D.