Question

Figure shows the behaviour of light rays with respect to a thin plano-convex lens whose plane surface is silvered as shown in the figure. If the refractive index of the material of the lens is 1.5. choose the correct option(s).

• A. The focal length of the silvered lens (which acts as a mirror) is 10 cm.
• B. Radius of curvature of the curved part of the lens is 10 cm.
• C. In the silvered lens, rays fall normally on the silvered surface.
• D. The focal length of the lens (without silvering) is 20 cm.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

The focal length of the silvered lens (which acts as a mirror) is 10 cm.

B

Radius of curvature of the curved part of the lens is 10 cm.

C

In the silvered lens, rays fall normally on the silvered surface.

D

The focal length of the lens (without silvering) is 20 cm.

As image coincides with the object, object lies on the 2F of the effective mirror
2F = 20 cm
F = 10 cm
$\frac{2}{f_L}=\frac{1}{f}\frac{2}{f_L}=\frac{1}{10}{f}_L=20cm\frac{1}{20}=\left(0.5\right)\left(\frac{1}{R}\right)$
R=10 cm
As the image coincides with the object, incident ray hits the silvered surface perpendicularly.