An object is placed in front of a convex mirror at a distance of `50cm`A p[lane mirror is introduced covering the lower half of the convex mirror.If the distance between the images formed by the two mirrors .The radius of the convex is :

Options

A. `12.5cm`
B. `25cm`
C. `50cm`
D. `100cm`

Answer

B

Explanation

Image of O in mirror will acts as object for concave mirror.

For plane mirror `v=-u rArr v=-(-30)cm rArr v=30cm`
For two images two be coincides ,image from convex mirror `v=10cm`
`(1)/(v)+(1)/(u)=(1)/(f) rArr (1)/(10)+(1)/(-50)=(1)/(f) rArr (1)/(f)=(5-1)/(50)`
f=12.5 `" " implies R= 2f`
R=25 cm