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.

Answer 1

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.