Question

A point object is placed at the center of a glass sphere of radius $6cm$ and refractive index $1.5$. The distance of virtual image from the surface is

• A. $6cm$
• B. $4cm$
• C. $12cm$
• D. $9cm$

Answer 1

The correct option is A $6cm$

Here, $u=-6cm,v=?,r=-6cm,{\mu }_1=1,\mu =1.5$

Using the formula of spherical refracting surface,

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

We have $\frac{1.5}{v}-\frac{1}{-6}=\frac{1.5-1}{-6}\Rightarrow v=-6cm$

Alternative method : The rays coming from the point object fall on the glass-air interface normally and hence pass undeviated. Therefore, if we retrace the path of the refracted rays backward, the image will be formed at the center only.