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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.

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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 = vu = -20-60 = 13

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

1f=1v-1u1f=1-20-1-601f=1-20+1601f=-3+160=-130
∴ 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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