Shown in Fig. is a vertically erect object placed on the optic axis at a distance `(5//2)f` from a concave mirror of focal length f. If a plane mirror is placed perpendicular to the optic axis at a distanc `(4//3)f` from the pole, facing concave mirror, find the position and nature of the final image formed.

Explanation

Two rays come from the tip of the object. They converge after reflection to form a real image at `I_(1)`.
Since the plane mirror is introduced in the mid, the reflected rays from the concave mirror get reflected by the plane mirror to form an image`I_(2)`. Infact `I_(2)` is the real image of teh image `I_(1)` of the object O, which serves as a virtual object to the mirror,
`1/u+1/v+1/frArr1/(-2.5f)+1/v=1/(-f)`
`rArr 1/v=-1/f+2/(5f)=-3/(5f)`
`rArr v=-5/3f`
(Negative sign indicates the image is left the mirror).
`rArr` The image `I_(1)` is formed which behaves as a virtual object for the plane mirror & therefore finally a real erect image `I_2` of same size, will be formed at equal distance x infront of the plane mirror as shown in the figure.
`rArr I_2` will be formed at a distance `(5//3)f-2x`, from concave mirror
where x=`5//3f-4//3f=1//3f`
`rArr ` The final image distance `v^' = (5//3)f-2(1//3f)=f`
`rArr` Final image i f formed at the focus.