Question

A 2.0 cm tall object is placed 40 cm from a diverging lens of focal length 15 cm. Find the position and size of the image.

Answer 1

A concave lens is also known as a diverging lens.
Focal length of concave lens, f = -15 cm
Object distance from the lens, u = -40 cm
Height of the object, h₁ = 2.0 cm
Height of the image, h_2 = ?
Using the lens formula, we get: 

`1/f=1/v-1/u` 

`1/-15=1/v-1/-40` 

`1/-15=1/v+1/40` 

`1/v=1/-15-1/40` 

`1/v=(-8-3)/120` 

`1/v=-11/120` 

∴ v = - 10.90 cm

Therefore, the image is formed at a distance of 10.90 cm and to the left of the lens.
Magnification of the lens: 

Magnification=`"Image distance"/"object distance"="Height  of the image"/"Height of the object"`  

`v/u=h_2/h_1` 

`-10.90/-40=h_2/2` 

h_2=+0.54

The height of the image formed is 0.54 cm. Also, the positive sign of the height of the image shows that the image is erect.