In the shown figure `M_(1)` and `M_(2)` are two concave mirrors of the same focal length `10 cm` . `AB` and `CD` are their pricipal axes respectively. `A` point object `O` is kept on the line `AB` at a distance `15 cm` from `M_(1)` . The distance between the mirror is `20 cm` . Considering two successive reflections first on `M_(1)` and then on `M_(2)` . The distance of final image from the line `AB` is:

Options

A. `3 cm`
B. `1.5 cm`
C. `4.5 cm`
D. `1 cm`

Answer

B

Explanation

For `M_(1)`
`v=(uf)/(u-f) =(-15xx(-10))/(-15-(-10))=-30 cm`
For `M_(2) u=10 cm`
`therefore v=(10xx(-10))/(10-(-10))=-5 cm`
magnification `m=(-v)/(u)=-((-5)/(10))=(1)/(2)`
so, distance of image from `CD=(1)/(2)xx3=(3)/(2) cm`
`therefore` distance of image from `AB=3-(3)/(2)=(3)/(2) cm`