Question

A concave mirror produces three times enlarged image of an object placed at 10 cm in front of it . Calculate the focal length of the mirror . ​

Answer 1

Answer:

m=3

u=10cm

f=?

m=-v/u

3=-v/10

v=-30cm

1/v+1/u=1/f

1/-30+1/10=-2/-30

1/f =1/15

f=15cm

Answer 2

Object distance, u = -10cm

Magnification, m = 3

We know that,

m = $\rm\frac{-v}{u}$

3 = $\rm\frac{-v}{-10}$

v = +30cm

By applying mirror's formula:

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

$\rm\frac{1}{f} = \frac{-1}{10} + \frac{1}{30}$

$\rm\frac{1}{f} = \frac{-3 + 1}{30}$

$\rm\frac{1}{f} = \frac{-2} {30}$

$\rm\frac{1}{f} = \frac{-1}{15}$

$\fbox{f = -15cm}$