Question

The distance between the object and real image formed by
a convex lens is D. If the magnification is M, then focal
length f is:
(a) M/(M-1)D
(b)M/(M+1)^2D
(c)M/(M-1)D
(d)M/(M+1)D​

Answer 1

Given : The distance between the object and real image formed by a convex lens is D. If the magnification is M.

To find : The focal length of convex lens.

solution : let object distance is u and image distance is v.

The distance between the object and image = v + u = D

⇒v = D - u .......(1)

again, magnification = M

⇒v/u = M

⇒v = Mu.........(2)

from equations (1) and (2) we get,

Mu = D - u

⇒u = D/(1 + M)

and v = Mu = MD/(1 + M)

using formula, 1/v - 1/u = 1/f

⇒1/{MD/(1 + M)} - 1/{-D/(1 + M)} = 1/f

⇒1/f = (1 + M)/MD + (1 + M)/D

⇒1/f = (1 + M) [1/MD + 1/D] = (1 + M)(1 + M)/MD

⇒f = [ M/(M + 1)² ]D

Therefore option (b) is correct choice

Answer 2

Answer: option b

Explanation: