On the axis of a spherical mirror of focal length `f` a short linear object of length `L` lies on the axis at a distance `mu` from the mirror. Its image has an axial length `L'` equal to

Options

A. `L[f/((mu-f))]^(1//2)`
B. `L[(mu+f))/f]^(1//2)`
C. `L[((mu-f))/f]^(2)`
D. `L[f/((mu-f))]^(2)`

Explanation

(d) For spherical mirror `v=(fu)/((u-f))`
The value of `u` for two ends of the objects of length `L` are
`u_(1)-mu-L/2` and `u_(2)=mu+L/2`
Then, the axial length of the image
`L'=v_(1)-v_(2)=(f(mu-L/2))/((mu-L/2-f))-(f(mu+L/2))/((mu+L/2-f))`
`=f[(Lf)/((mu-f)^(2)-(L^(2))/4)]=L[f/(mu-f)]^(2)`