Question

A spherical convex surface of power $5$ dioptre separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is

• A. 20 cm
• B. 1 cm
• C. 4 cm
• D. 5 cm

Answer 1

Answer: (D)

$P=5\, D$
$u=\infty$ then
$\frac{1}{\infty}-\frac{4 / 3}{f}=\frac{1-4 / 3}{R}$
$-\frac{4}{3 f}=-\frac{1}{3 R}$
$\frac{f}{4}=R$
$f=4\, R$
$\therefore \frac{100}{5}=4\, R$
$ \Rightarrow R=\frac{25}{5}=5\, cm$