Question

A mirror  forms an image which is 30 cm from an object  and twice its height.Find  the object distance and its centre of curvature.

Answer 1

Hey,

Given that a magnified image is formed by the spherical mirror.

The given condition is possible only when the object is placed between the focus and the pole of the concave mirror.


Suppose, -u is the object distance, +v is the image distance and -f is the focal length.
m = -v/u = 2
v = -2u ---------------(1)
Also,
-u + v = 30 --------- (Now substitute (1) here)
-3u = 30
u = -10
And v = 20

HOPE IT HELPS:-))

Now, 1/v + 1/u = 1/f
1/20 - 1/10 = 1/f
Therefore, f = -20


So, the object distance is -10 cm and the center of curvature is at -40 cm.

Answer 2

Given:
v - u = 30 cm
Hₐ = Height of object
Hₓ = Height of Image
Hₓ = 2Hₐ

Solution:
Hₓ/Hₐ = 2 = Magnification
Also Magnification = -v/u
                          2  = -v/u
                          -v = 2u
                           v = -2u
Then in v + u = 30
          -2u - u = 30
                -3u = 30 cm
                    u = -10 cm
And so         v = 20 cm

Then Mirror formula 
  1/f = 1/v + 1/u
  1/f = 1/20 + 1/-10
  1/f = 1 - 2/20
  1/f = -1/20
     f = -20 cm

Then u = -10 cm
          v = 20 cm
     COC = 2(20) = 40 cm                                 (COC - Centre of Curvature)


:) Hope this Helps !!!