An object placed 20 cm in front of a mirror is found to have an image 15 cm (*a*) in front of it, (*b*) behind the mirror. Find the focal length of the mirror and the kind of mirror in each case.

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#### Solution

Distance of the object 'u' = -20 cm

Image is formed in front of the mirror at a distance (v) of -15 cm.

Therefore, the focal length of the mirror 'f' is

⇒`1/f=1/v+1/u`

⇒`1/f=1/-15+1/-20`

⇒`1/f=-4/60-3/60=(-7)/60`

⇒`f=(-60)/7 cm `

Thus, the mirror is concave and has a focal length of 60/7.

(ii) Distance of the object 'u' = -20 cm

Image is formed behind the mirror at a distance (v) of 15 cm.

Then, the focal length of the mirror 'f' will be

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

⇒`1/f=1/15+1/-20`

⇒`1/f=4/60-3/60=1/60`

⇒`f=60 cm `

Thus, the mirror is convex and has a focal length of 60 cm.

Concept: Convex Mirror

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