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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.
Solution
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 .
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