Two objects `A` and `B`, when placed one after another in front of a conacve mirror of focal length `10 cm`, from images of same size. Size of object `A` is four times that of `B`. If object `A` is placed at a distance of `50 cm` from the mirror, what should be the distance of `B` from the mirror ?

Answer

`-20 cm`

Explanation

For object `A`, `m' = (h'_(2))/(h'_(1)) = (f)/(f - u_(2))`
`:. (m)/(m') = (h_(2))/(h_(1)) xx (h'_(1))/(h'_(2)) = (f - u_(2))/(f - u_(1))`
Now, `h_(1) = 4 h_(1)` , `h_(2) = h'_(2)`, `f = - 10 cm`,
`u_(1) = - 50 cm`
`:. (h'_(1))/(4 h'_(1)) = (- 10 - u_(2))/(- 10 + 50)`
`- 40 - 4 u_(2) = 40`
`- 4u_(2) = 80, u_(2) = - 20 cm`