Question

two lenses of power 3D and -5 combined to form compound is an object is placed at a distance of 50 cm from the lens calculate the position of its image

Answer 1

Answer: -25 cm

Explanation:

The power of two lenses are given as P1 = +3D & P2 = - 5D

Object distance, u = -50 cm

Since the two lenses are combined to form a composite lens, therefore,

The power of the combination lens, P = P1+P2 = +3 + (-5) = 3 – 5 = - 2 D

We know, the formula for the power of a lens is given as,

P = 1/f

Rearranging the formula

⇒ f = 1/P = 1/(-2) = - 0.5 m = - 50 cm

So, the combination lens will act like a concave lens with focal length f = - 50 cm and object distance u = -50 cm.

Using the lens formula,  

1/f = 1/v - 1/u

⇒ 1/v = 1/f + 1/u  

⇒ 1/v = [1/(-50)] + [1/(-50)]

⇒ 1/v = [-1-1]/50

taking the reciprocal

⇒ v = -50/2 = -25 cm

Thus, the virtual image will be formed at a distance of 25 cm.