An object `2 cm` high is placed at a distance of `16 cm` from a concave mirror, which produces a real image `3 cm` high. What is thr focal length of the mirror ? Find the position of the image ?

Answer

`f = - 9.6 cm, v = -24 cm`

Explanation

Here, `h_1 = 2 cm, u = -16 cm`,
`h_2 = - 3 cm` (because image is real and inverted)
As `(- h_2)/(h_1) = (v)/(u)`
`:. v = (-h_2)/(h_1) u = (3)/(2) xx (-16) = -24 cm`
`(1)/(f)=(1)/(v)+(1)/(u) = (1)/(-24) -(1)/(16) = (-2 -3)/(48) = - (5)/(48)`
`f = - (48)/(5) = - 9.6 cm`.