Question

The radius of curvature of a concave mirror is 40 cm. Find position of an object in front of the mirror, so that its real image is two times the size of the object.

Answer 1

Answer:

Convex mirror:

R = + 40 cm which means f = +20 cm

m = h 2/h 1 = 1/2 (magnification of convex mirror is positive)

Now m = -v/u = 1/2 >> u = -2 v

Mirror formula :

1/f = 1/u +1/v

1/20 = 1/-2 v +1/v

1/20 = (-1+2)/2 v

v = 10 cm and u = -20 cm

Answer 2

Concave Mirror

r = 2f

f = - 40/2

f = - 20 cm

m = hi/ho = -v/u

m = -2 (image will be formed below principal axis)

-2 = -v/u

2u = v

Using mirror formula

1/f = 1/u + 1/v

-1/20 = 1/u + 1/2u

1/20 = - 3/2u

u = - 30 cm

v = - 60 cm