Question

An object 60 cm from a lens gives a virtual image at a distance of 20 cm in front of the lens. What is the focal length of the lens? Is the lens converging or diverging? Give reasons for your answer.

Answer 1

Object distance  u = - 60 cm (As the object is on the left side of the lens)
Image distance v = - 20 cm (As the image is virtual) 

Magnification `m=v/u=(-20)/-60=1/3` 

Because the image is diminished and virtual, the lens is concave and diverging in nature.
Using the lens formula: 

`1/f=1/v-1/u` 

`1/f=1/-20-1/-60` 

`1/f=1/-20+1/60` 

`1/f=(-3+1)/60=-1/30`

∴ f = - 30 cm.
Therefore, the focal length of the lens is 30 cm.
The lens is diverging in nature because a negative focal length indicates a concave lens .