Question

A point object is situated at a distance of $40cm$ from the centre of the sphere of radius $20cm$ and refractive index $1.5$. Locate the position of the image due to refraction through the sphere.

• A. $30$ cm from the surface
• B. $36$ cm from the centre
• C. $30$ cm from the centre
• D. Both (1)& (2)

Answer 1

The correct option is C $30$ cm from the centre

Here,

$n_1=1$

$n_2=1.5$

$R=-20cm$

$u=-40cm$

Now using the formula,

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$⟹\frac{1.5}{v}-\frac{1}{-40}=\frac{1.5-1}{-20}=-\frac{0.5}{20}$

$⟹\frac{1.5}{v}+\frac{1}{40}=-\frac{1}{40}$

$⟹\frac{1.5}{v}=-\frac{1}{40}-\frac{1}{40}$

$⟹\frac{1.5}{v}=-\frac{1}{20}$

$⟹v=-30cm$

So the image is $30cm$ away from the center of the sphere.