A concave mirrorr of focal length `15 cm` forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be

Options

A. `7.5 cm`
B. `22.5 cm`
C. `40 cm`
D. `30 cm`

Answer

A

Explanation

Image formation by concave mirror will be as follows:

Given, `m = ("image distance")/("object distance") = - (v)/(u) =2`
`rArr =-2u`
Also `(1)/(f) = (1)/(v) + (1)/(u)`
where `f` is focal length, `v` is image distance and `u` is object distance.
`rArr -(1)/(15) = (1)/(u)-(1)/(2u) = (1)/(2u)`
`rArr u = -(15)/(2) =-7.5cm`
Thus, the object should be placed at distance `7.5 cm` in front of the mirror.