Question

A lens of focal length 12 cm forms an erect image three times the size of the object. The distance between the object and image is ______.

Options

• 8 cm

• 16 cm

• 24 cm

• 36 cm

Answer 1

A lens of focal length 12 cm forms an erect image three times the size of the object. The distance between the object and image is 16 cm.

Explanation:

Given:

Magnification, M = 3

Focal length f = 12 cm

Image distance v = ?

Object distance u = ?

We know that:          

`M = v/u`

Therefore

`3 = v/u`

3u = v

Putting these values in the lens formula, we get: 

`1/v-1/u = 1/f` 

⇒ `1/(3u)-1/u = 1/12` 

⇒ `(1-3)/(3u) = 1/12` 

⇒ `(-2)/(3u) = 1/12` 

⇒`3u = −24` 

⇒ `u = (-24)/3` 

⇒ u = −8 cm 

v = 3u = −8 × 3 = −24 cm

The distance between the object and image is

∣v − u∣ = ∣−24 − (−8)∣ = ∣−24 + 8∣ = ∣−16∣ = 16cm.

The distance between the object and image is 16 cm.