A plane mirrorr is placed `22.5cm` in front of a concave mirrorr of focal length `10cm`. Find where an object can be placed between the two mirrorrs, so that the first image in both the mirrorrs coincides.

Explanation

Let object be placed at distance x from plane mirror as shown. The image is formed at distance `(22.5+x)` for concave mirror.
`u=-(22.5-x),v=-(22.5+x),f=-10cm`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(-(22.5+x))+(1)/(-(22.5-x))=(1)/(-10)`
`(45)/((22.5^2-x^2))=(1)/(10)`
`22.5^2-x^2=450`
`x^2=22.5^2-450=56.25`
`x=7.5cm`