A concave mirror is making a highly diminished image of an object AB that is kept very far away. If the image is 10 cm away from the mirror, what is the radius of curvature of the given mirror?

-20 cm

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+20 cm

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+10 cm

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-10 cm

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Solution

The correct option is A -20 cm
For an object kept at infinity, a concave mirror forms an image at its focal point. As shown in the diagram, the focal point is 10 cm away from the pole in the opposite direction of the incident ray. Hence the focal length of the given mirror is -10 cm.

For a spherical mirror, we also know that,
Radius of curvature, $R = 2 f$
(where f is focal length)

Hence,
Radius of curvature, $R = 2 \times (- 10) = - 20 c m$

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