Question

The focal length of a convex lens is 18 cm and the size of the image is a quarter of the object. The object is situated at a distance of (a) 90 cm (b) 54 cm (c) 22.5 cm (d) 60 cm
​

Answer 1

Given: The focal length of a convex lens is provided to be 18 cm. Also, the magnification is given as 1/4 and we are asked to find the object distance.

Concept: Focal length of a convex lens is +ve. Also, the magnification of a spherical lens is the ratio of image distance (v) to the object distance (u).

• m = v/u
• 1/4 = v/u
• v = u/4

where, m, v and u represents magnification, image distance and object distance

lens formula is as follows:

• 1/f = 1/v + 1/u

where, f, v and u represents focal length, image distance and object distance.

Calculation:

⇒ 1/18 = 4/u + 1/u

⇒ 1/18 = 5/u

⇒ 18 = u/5

⇒ u = 18 × 5

∴ u = 90 cm

_______________________