An object 3 cm high is placed at a distance of 8 cm from a concave mirror which produces a virtual image 4.5 cm high:

(i) What is the focal length of the mirror?

(ii) What is the position of image?

(iii) Draw a ray-diagram to show the formation of image.

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#### Solution

Distance of the object from the mirror '*u*' = -8 cm

Height of the object '*h*_{o}' = 3 cm

Height of the image '*h*_{i}' = 4.5 cm

We have to find the focal length of the mirror '*f*' and distance of the image '*v*'.

Using the magnification formula, we get

`m=h_i/h-o=-v/u`

`m4.5/3=(-v)/(-8)`

`v=4.5xx8/3=12`cm

Therefore, the distance of the image '*v*' is 12 cm behind the mirror.

Now, using the mirror formula, we get

`1/f=1/v+1/u=1/12+1/-8`

`1/f=2/24-3/24=-1/24`

f =-24 cm

Thus, the focal length of the concave mirror '

*f*' is 24 cm.

Concept: Concave Mirror

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