Q. A thin plano-convex lens acts like a concave mirror of focal length 0.2 m when silvered from its plane surface. The refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface the lens will be
A) 0.1 m
B) 0.75 m
C) 0.4 m
D) 0.2 m
Explanation
(d) After silvering the plane surface, plano convex lens behave as a concave mirror of focal length
$\frac{1}{F} = \frac{2}{f_{lens}}$
$but\ \ \ F = 0.2\ m$
$\therefore\ f_{lens} = 2F = 2 \times 0.2 = 0.4\ m$
Now, from lens maker’s formula
$\frac{1}{f_{lens}} = (\mu - 1)(\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$\therefore\frac{1}{0.4} = (1.5 - 1)(\frac{1}{R_{1}} - \frac{1}{\infty})$
$\Longrightarrow R_{1} = 0.5 \times 0.4 = 0.2\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.