When the distance of an object from a concave mirror is decreased from `15 cm` to 9 cm, the image gets magnified `3` times than that in first case. Calculate focal length of the mirror.

Answer

`- 6 cm`

Explanation

In first case, `u = - 15 cm`
`m' = (f)/(f - u) = (f)/(f + 15)`
In second case, `u = - 9 cm`
`m' = (f)/(f - u) = (f)/(f + 9)`
As `m' = 3 m`
`:. (f)/(f - 9) = (3 f)/(f + 15)` or `3f + 27 = f + 15`
`f = -6 cm`.