Question

A plano-convex lens of refractive index $1.5$ and radius of curvature $30cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. The distance from this lens, an object be placed in order to have a real image of the size of the object is

• A. $20cm$
• B. $30cm$
• C. $60cm$
• D. $80cm$

Answer 1

Answer: (A)

A plano-convex lens behaves like a concave mirror when its curved surface is silvered.
$\therefore$ $\text{F}$ of the concave mirror so formed
$=\frac{\text{R}}{2\mu }=\frac{\text{30}}{2\times \text{1.5}}$ $=10cm$
To form an image of object size, the object should be placed at $\left(2\text{F}\right)$ of the concave mirror.
$\therefore$ The distance of the object from the lens $=2\times \text{F}$
$=2\times \text{10}=$ $20cm.$