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# 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. - CBSE Class 10 - Science

ConceptReflection of Light Image Formation by Spherical Mirrors - Concave Mirror

#### 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.

#### 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=(-v)/u

3=(-v)/-10

v=30 cm

Thus, the distance of the image 'v' is 30 cm behind the mirror.Now, using the mirror formula, we get

1/f=1/v+1/u

1/f=1/30+1/-10

or 1/f=1/30-3/30=(-2)/30

or 1/f=-1/15

or f =-15 cm Thus, 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 cm

Radius of curvature of the mirror is 30 cm.

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Solution 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. Concept: Reflection of Light - Image Formation by Spherical Mirrors - Concave Mirror.
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