Express the magnification produced by a lens in terms of the local length of the lens and (1) the object distance (2) The image distance.

Explanation

Magnification (M) produced by a lens
`(h_(2) "(height of the image)")/(h_(2)"(height of the object)")`
`(v "(image distance)")/(u"(object distance)")`
Now, `1/v-1/u =1/f" "…` (Lens formula)
Where f is the focal length of the lens
`therefore u/v -u/v =u/f" "...` (1)
and `(v)/(u)- v/u =u/f " "...(2)`
(1) from Eq. (1) , we have
`u/v-1 =u/f`
`therefore u/v =u/f +1 =(u-f)/(f)`
`therefore M=v/u =f/(u+f)`
(2) From Eq. (2) , we have
`1-v/u =v/f therefore v/u=1-v/f =(f-v)/(f)`
`therefore M=v/u=(f-v)/(f)`