Question

The position of an image for the object $O$ is at a distance $nR$ on the concave side of spherical refracting surface from the point $P$ shown in figure. There are two different media present on both sides of spherical surface. The value of $n$ will be :
($R$ is the radius of curvature of the spherical surface).

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$


Given,
${\mu }_1=1$
${\mu }_2=1.5$
$u=-5R$

Radius of curvature is $+R$, because the centre of circle of which the spherical surface is a part lies in the direction of incident ray.

Also, $v=+nR$ as per the sign convention.

Using relation between object & image distances for refraction at curved surfaces:

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

$\Rightarrow$ $\frac{1.5}{nR}-\frac{1}{(-5R)}=\frac{1.5-1}{R}$

$\Rightarrow \frac{1.5}{n}+\frac{1}{5}=0.5$

$\Rightarrow \frac{1.5}{n}=0.5-0.2=0.3$

$\therefore n=5$

Why this question? $\underset{–}{\text{Caution}}$: While using this formula, be careful with the sign of the object distance, image distance and radius of curvature. The sign convention must be strictly followed to avoid any errors.