If a concave mirror has a focal length of 10 cm, find the two positions where an object can be placed to give, in each case, an image twice the height of the object.

#### Solution

Given,

Focal length (f) of the concave mirror = -10 cm__Case-1 __

The image is real, and its magnification (m) is -2.

Using the magnification formula, we get

`1-10=12u+1u`

`m=(-v)/u`

`-2=(-v)/u`

v=2u

Now, using the mirror formula, we get

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

`1/-10=1/2u+1/u`

`1/-10=1/(2u)+2/(2u)=3/2u`

`u=(3xx(-10))/2=-15 cm

The object should be placed at a distance of 15cm from the concave mirror.

__Case-2__

The image is virtual and has a magnification 'm' of 2.

Using the magnification formula, we get

`m=-v/u`

`2=-v/u`

v=-2u

Now, using the mirror formula, we get

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

`1/-10=1/(-2u)+1/u`

`1/-10=-1/(2u)+2/(2u)=1/(2u)`

`u=(-10)/2=-5 cm `

Thus, the object should be placed at a distance of 5 cm in front of the concave mirror.