An object is placed `18 cm` in front of a mirror. If the image is formed at `4 cm` to the right of the mirror, calculate its focal length. Is the mirror convex or concave ? What is the nature of the image ? What is the radius of curvature of the mirror ?

Explanation

Here, `u = -18 cm, v = 4 cm, f = ?`
From `(1)/(f)=(1)/(v)+(1)/(u)=(1)/(4)-(1)/(18)=(9 - 2)/(36) = (7)/(36)`
`f = (36)/(7) = 5.14 cm`
As focal length is positive, the mirror must be convex. The image is virtual, erect and smaller in size.
`R = 2f = 2 xx 5.14 cm = 10.28 cm`.