Question

A mark placed on the surface of a sphere is viewed through glass from a position directly opposite as shown in the figure. The diameter of the sphere is $30\, cm$ and refractive index of glass is $1.5$. The position of the image is

• A. at a distance of $60 \, cm$ from surface $A B C$ in the direction of incident light
• B. at a distance of $60\, cm$ from the surface $A B C$ opposite to the direction of incident light
• C. at a distance of $30 \, cm$ from the surface $A O C$ opposite to the direction of incident light on $A B C$
• D. Both (b) and (c)

Answer 1

Answer: (B)

Given, for refraction at spherical surface $A B C$,

$u =2 R=-30 \,cm $
$ \mu_{1} =1.5 $
$ \Rightarrow \mu_{2}=1.0 $
$ v =?$
Applying, $\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$
$\frac{1}{v}-\frac{1.5}{(-30)}=\frac{(1-1.5)}{(-15)}$
$\Rightarrow \frac{1}{v}+\frac{1.5}{30}=\frac{-0.5}{-15}$
$ \Rightarrow \frac{1}{v}=\frac{0.5}{15}-\frac{1.5}{30}$
$\Rightarrow v=-60 \,cm$
The image is at a distance of $60\, cm$ from surface $A B C$ opposite to the direction of incident light.