The distance between an object and its doubly magnified image by a concave mirror is: [Assume `f`= focal length]

Options

A. `3 f//2`
B. `2 f//3`
C. `3 f`
D. depends on whether the image is real or virtual.

Answer

A

Explanation

For `m=2`
`m=(v)/(u)=2`
`V=-2u` ………………..`(i)`
`(1)/(f)=(1)/(v)+(1)/(u) rArr (1)/(f)=(1)/(-2u)+(1)/(u)`
`rArr (1)/(f)=(1)/(2u) rArr u=(f)/(2)`
`& v=-f`
Distance between object `&` image `=f+f//2=3f//2`
For `m=-2`
`m=-(v)/(u)=-2`
`v=2u`
`rArr (1)/(f)=(1)/(2u)+(1)/(u) rArr u=(3f)/(2)`
`& v=3f`
Distance between object `&` image `=3f-(3f)/(2)` .