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Question

A concave mirror produces three times enlarged virtual image of an object placed at 10 cm in front of it. Calculate the radius of curvature of the mirror.

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Solution

Given,
Distance of the object 'u' = -10 cm

Magnification 'm' = 3
We have to find the focal length 'f' and the radius of curvature 'R'.

Using the magnification formula, we get
m=-vu3=-v-10v=30 cmThus, the distance of the image 'v' is 30 cm behind the mirror.Now, using the mirror formula, we get 1f=1v+1u 1f=130+1-10or 1f=130-330=-230or 1f=-115or f=-15 cmThus, the focal length of the mirror 'f' is -15 cm.Therefore, the radius of curvature of the mirror 'R' will be 2f=2×-15 =-30 cmRadius of curvature of the mirror is 30 cm.

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