Question

A spherical convex surface of radius of curvature $10\text{cm}$ has object and image in mediums of refractive index $1.0$ and $\frac{4}{3}$ respectively. Its power will be

• A. $+4\text{D}$
• B. $+6\text{D}$
• C. $+1\text{D}$
• D. $+3.33\text{D}$

Answer 1

The correct option is D $+3.33\text{D}$

We know that, if rays are parallel to the principal axis, object is at infinite distance and image formed is at focal point.

For spherical convex surface, using
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$



$\frac{\frac{4}{3}}{f}-\frac{1.0}{\infty }=\frac{\frac{4}{3}-1}{10}$

$\Rightarrow f=40\text{cm}\text{or}0.4\text{m}$

Since the rays are converging, its power should be positive.

we know that, Refracting power of spherical surface is defined as the reciprocal of the reduced focal length.

$\therefore$ Power of refracting surface, $P=\frac{{\mu }_2}{f}$
$\Rightarrow P=\frac{4/3}{0.4}=+3.33\text{D}$

Hence, option (d) is the correct answer.