A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror:

(i) Calculate the image distance.

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

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#### Solution

A concave mirror is a converging mirror.

Distance of the object from the mirror '

*u*' = -20 cmHeight of the object '

*h*' = 1 cm_{o}Height of the image '

We have to find the distance of the image '

*h*' = -4 cm_{i}We have to find the distance of the image '

*v*' and focal length of the mirror '*f*'.Using the magnification formula, we get

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

`-4/1=-v/-20`

`v=20xx-4/1=-80` cm

Thus, the distance of the image '*v*' is 80 cm.

Now, using the mirror formula, we get

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

`1/f=1/-80+1/-20=-1/80-4/80=-5/80`

`1/f=-1/16`

f=-16 cm

Thus, the focal length of the concave mirror is 16 cm.

Concept: Concave Mirror

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