#### Question

A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.

#### Solution

Distance of the object from the mirror (u) = -5 cm

Height of the image (h_{i}) = -1 cm

Height of the object (h_{o}) = 2.5 mm = 0.25 cm

We have to find the image distance (v) and the focal length of the mirror (f).

Using the magnification formula, we get

`m=h_i/h_o=(-v)/u`

`or (-1)/0.25=(-v)/-5`

`or v=-5/0.25=-20 `cm

Thus, the distance of the image is -20 cm.

It means that the image will form 20 cm in front of the mirror.

Now, using the mirror formula, we get

`1/f=1/v+1/u`

`1/f=1/-20+1/5`

`or1/f=1/20+1/-5`

`or 1/f=-1/20-4/20=-5/20=-1/4`

f=-4 m

Thus, the focal length of the mirror is 4 cm.