#### Question

At what distance from a concave mirror focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

#### Solution

Height of the object '*h** _{o}*' = 2 cm

Focal length of the mirror '*f*' = −10 cm

Height of the image '*h _{i}*' = 6 cm

We have to find the distance of the object from the mirror '

*u*'.

Using the magnification formula, we get

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

`m=6/2=-v/u`

`m=3=-v/u`

thus v=-3u

Now, using the mirror formula, we get

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

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

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

`u=(-2xx10)/3`

u=-6.67 cm

Thus, the distance of the object from the mirror '*u*' is −6.67 cm.

Is there an error in this question or solution?

Solution At What Distance from a Concave Mirror Focal Length 10 Cm Should an Object 2 Cm Long Be Placed in Order to Get an Erect Image 6 Cm Tall? Concept: Representation of Images Formed by Spherical Mirrors Using Ray Diagrams - Concave Mirror.