Question

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
A. 45 cm
B. 30 cm
C. `7.5 cm`
D. `22.5 cm`

Answer 1

Correct Answer - C
Focal length of concave mirror `f = - 15 cm`
magnification `=2`(for virtual image)
Linear magnification `m=("size of image")/("size of object") =-(upsilon)/(u)`
`2=-(upsilon)/(u)` or `upsilon=-2u`
Now, from the relation
`(1)/(f)=(1)/(upsilon)+(1)/(u)`
Or `(1)/(15)=(1)/(u)-(1)/(2u)=(1)/(2u)`
or `2u =- 15` or `u = -7.5 cm`.