Question

The magnification of an object placed in front of a convex lens of focal length 20 cm is +2. To obtain a magnification of -2, the object has to be moved a distance equal to
A) 10cm
b) 20cm
c) 30cm
d) 40cm ​

Answer 1

Answer: (b) 20 cm.

Explanation:

We know, lens formula:

1/v - 1/u = 1/f

As, m = v/u => v = mu

∴ 1/mu - 1/u = 1/f

=> 1/u(1/m - 1) = 1/f

=> 1/m = u/f + 1

=> m = f/(f + u)

Case 1:

Let, the initial object distance be = u.

f = + 20 cm

m = + 2

∴ 2 = 20/(20 + u)

=> 1 = 10/(20 + u)

=> u = 10 - 20 = - 10 cm

Case 2:

Again, let final object distance = u′

And, m′ = - 2

∴ m′ = f/(f + u′)

=> - 2 = 20/(20 + u′)

=> - 1 = 10/(20 + u′)

=> - u′ - 20 = 10

=> u′ = - 30 cm

So, object has moved through a distance of u′ - u = 30 - 10 = 20 cm.