Magnitude of focal length of a spherical mirror is f and magnitude of linear magnification is `1/2`

Options

A. If image is inverted, it is a concave mirror
B. If image is erect, it is a convex mirror
C. Object distance from the mirror may be `3 f`
D. Object distance from the mirror may be f.

Answer

A, B, C, D

Explanation

Inverted and real image is formed by concave mirror.
Let `u= -x` , then `v= +(x/2)`
`:. (1)/(+x//2) +(1)/(-x)=(1)/(+f)`
`:.x=3f`
Erect and virtual image is formed by convex mirror.
let `u=-x`, then `v= +(x/2)`
`(1/(-x//2))+(1)/(-x)=(1)/(+f)`
`x= +f`.