Question

3. A concave mirror produces four times magnified real
image of a real object. If the distance between object
and its image is 60 cm, then the value of radius of
curvature of the mirror is​

Answer 1

Answer:

The radius of curvature of concave mirror is -32 cm.

Explanation:

Given that

Magnification m = -v/u

                           = -4 cm ( since the focal length of concave mirror is taken as negative)

Distance between object 'u' and image 'v' = 60 cm

                                                              v - u = - 60 cm ( Since v & u is always taken as negative for concave mirror according to sign convention)

From magnification, m = -v/u

                                  -4 = (60 -u)/u  (from given equation v - u = 60, -v = 60 - u)

                                 -4u = 60 - u

                                 3u = -60

                                   u = -20 cm

Therefore,

                                   v = - 80 cm  ( Substituting in v -u = -60 cm)

From mirror formula

                                  $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

                                  $\frac{1}{f} = \frac{1}{-20} + \frac{1}{-80}$  

On solving for 'f' we get

                                   f = -16 cm

Therefore,

                    Radius of curvature, R = 2f

                                                          = 2 x -16

                                                          = -32 cm

So, the value of radius of curvature of concave mirror is - 32 cm.