As object is placed exactly midway between a concave mirror of `R = 40 cm` and a convex mirror of `R = 30 cm`. The mirrors face eachother and are `50cm` apart. Determine the nature and position of image formed by successive reflections first at concave mirror and then at convex mirror.

Explanation

The course of rays for image formation is shown in Fig.

(i) For concave mirror :
`f_(1) = -25 cm`.
`(1)/(v_(1)) = (1)/(f_(1)) - (1)/(u_(1)) = (1)/(-20) + (1)/(25) = -(1)/(100)`
`v_(1) = -100 cm`
As `v_(1)` is negative, image `A'B'` formed by concave mirror is real, formed in front of concave mirror such that `P_(1)B' = 100 cm`.
(ii) For convex mirror : `A'B'` acts as a virtual object
`u_(2) = P_(2)B' = P_(1)B' - P_(1)P_(2) = 100 - 50 = 50 cm`,
`f_(2) = (R_(2))/(2) = (30)/(2) = 15 cm`
`(1)/(v_(2)) = (1)/(f_(2)) - (1)/(u_(2)) = (1)/(15) - (1)/(50) = (7)/(150)`
`:. v_(2) = (150)/(7) = 21.43 cm`
As `v_(2)` is positive, final image `A"B"` is virtual and is fromed behind the convex mirror, such that `P_(2)B" = 21.43 cm`.