Question

An object O is placed at a distance of 20 cm from a thin plano-convex lens of a focal length of 15 cm. The place surface of the lens is silvered as shown in the figure. The image is formed at a distance of ______.

 

Options

• 60 cm to the right of the lens.

• 30 cm to the left of the lens.

• 24 cm to the right of the lens.

• 12 cm to the left of the lens.

Answer 1

An object O is placed at a distance of 20 cm from a thin plano-convex lens of a focal length of 15 cm. The place surface of the lens is silvered as shown in the figure. The image is formed at a distance of 12 cm to the left of the lens.

Explanation:

The effective focal length of the silvered lens is given by,

`1/F = 2/f + 1/f_m = 2/15 + 1/∞ = 2/15`

which gives F = `15/2` cm. The silvered lens behaves like a concave mirror. Using the spherical mirror formula `1/v + 1/u = 1/F`, we have 

(∴ u = -20 cm and F = -15/2 cm)

`1/v + 1/(-20) = 2/(-15)`

which give v = -12 cm. The negative sign indicates that the image is formed to the left of the lens.