Question

An object is placed at a distance of 10 cm (in a medium of $\mu =1$) from the pole of a spherical refracting surface bounding a medium of $\mu =1.5$. If the image formed is virtual and at a distance of 40 cm, the spherical surface is -

• A. concave with radius of curvature=8 cm
• B. convex with radius of curvature=8 cm
• C. concave with radius of curvature=3.6 cm
• D. convex with radius of curvature=3.6 cm

Answer 1

The correct option is B convex with radius of curvature=8 cm

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\Rightarrow \frac{1.5}{\left(-40\right)}-\frac{1}{\left(-10\right)}=\frac{0.5}{R}$

$\Rightarrow \frac{-1.5}{40}+\frac{1}{10}=\frac{0.5}{R}$

$\Rightarrow \frac{-1.5}{40}+\frac{4}{40}=\frac{0.5}{R}$

$\Rightarrow \frac{2.5}{40}=\frac{0.5}{R}$

$\Rightarrow R=+8cm$

Since radius is $(+)$

$\therefore$ surface is convex

Hence,

option $\left(B\right)$ is correct answer.