Question

A concave mirror 3 times produce in large image of an object placed at 10 CM in front of it. Calculate the radius of curvature of the mirror

Answer 1

Answer:

(a) The image formed in front of the concave mirror is real, so m is negative,

m = -3, u = -10 cm

As m = -v/u or -3 = -v/-10

v = -30 cm

By mirror formula,

1/f = 1/v + 1/u = 1/-30 + 1/-10 = -4/30

or f = -30/4 = -7.5 cm

Radius of curvature, R = 2f = 2 x (-7.5) = 15cm

Answer 2

The mirror produces three times enlarged image.

So, magnification(m) = 3

WE KNOW, magnification of spherical mirrors = m = -v/u

Where v is the distance between image and mirror and u is the distance between object and mirror.

Here, u = -10 cm

=> 3 = -V/-10

=>v = 30

So , the distance between image and mirror = 30 cm

1/v + 1/u = 1/f(mirror formula)

1/30 + 1/-10 = 1/f

1/30 - 1/10 = 1/f

1/30 - 1/10 = 1/f

-2/30 = 1/f

-1/15 = 1/f

f = -15 cm

We know radius of curvature = 2f

So, radius of curvature = R = 2*-15 = -30 cm which is the required answer.