A luminous object is placed at a distance of `30 cm` from the convex lens of focal length `20 cm`. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature `10 cm` be placed in order to have an upright image of the object coincident with it ?

Options

A. `12 cm`
B. `30 cm`
C. `50 cm`
D. `60 cm`

Answer

C

Explanation

Here, `u = OC = - 30 cm, f = 20 cm`.
`(1)/(v) = (1)/(f) + (1)/(u) = (1)/(20) - (1)/(30) = (1)/(60)`
`v = 60 cm`.
To obtain upright image of `O` at `O` itself,
`v = OC_(1) = x + 10`
`:. x = v - 10 = 60 - 10 = 50 cm`