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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

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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.

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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