The distance between an object and its real image formed by a lens is D. If the magnification is `m`, the focal length of the lens is

Options

A. `((m-1)D)/(m)`
B. `(mD)/((m+1))`
C. `((m-1)D)/(m^2)`
D. `(mD)/((m+1)^2)`

Answer

D

Explanation

`u=-x,v=D-x,m=-m`
`m=(v)/(u)`
`-m=(D-x)/(-x)`
`(m+1)x=Dimpliesx=(mD)/(m+1)`
`D-x=D-(D)/(m+1)=(mD)/(m+1)`
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(D-x)-(1)/(-x)=(1)/(D-x)+(1)/(x)`
`=(m+1)/(mD)+(m+1)/(D)=(m+1)((m+1))/(mD)`
`f=(mD)/((m+1)^2)`