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

### Given

The concave mirror produces three times enlarged image of an object placed at 10cm in front of it.

### Find out

We need to find out the focal length of the mirror

### Solution

As per the given conditions,

m = 3 {A concave mirror produces three times enlarged image of an object and the }

u = -10 cm

### Formula

We know that,

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

Substituting the known values we get,

3 = (-v)/(-10)

v =  30

The distance between the mirror and image =   30 cm

From mirror formula, we know

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

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

(-2)/30 = 1/f

or f = – 15

The radius of curvature R = 2f

∴ R = 2 × (- 15)

R = -30 cm