Question

A plano-convex lens, made of glass (n = 1.5) has a curved surface whose radius is 40 cm. The image formed of an object is of the same size as that of the object. The distance of the object from the lens is ______.

Options

• 40 cm

• 80 cm

• 160 cm

• 200 cm

Answer 1

A plano-convex lens, made of glass (n = 1.5) has a curved surface whose radius is 40 cm. The image formed of an object is of the same size as that of the object. The distance of the object from the lens is 60 cm.

Explanation:

When a lens forms an image equal in size to the object, the magnification is 1.

u = 2f

This occurs when the object is positioned at twice the focal length of a convex lens.

Therefore, we first determine the focal length using the lens maker’s formula.

For a plano-convex lens:

`1/f = (mu - 1) (1/R - 0)`

= `(1.5 - 1) (1/40)`

= `0.5 (1/40)`

= `0.5/80`

= `1/80`

`1/f = 1/80`

f = 80 cm

Condition for same size image 

u = 2f

= 2 × 80

= 160 cm