The divergent lens in m linear magnification produced by the lens is

Options

A. m
B. `(1)/(m)`
C. `(m+1)`
D. `(1)/(m+1)`

Answer

D

Explanation

For a divergent lens, f : -ve, u : -ve
and `u= -mf or (1)/(u) = -(1)/(mf)`
Using the lens formula, `(1)/(v)-(1)/(u)=(1)/(f)`, we get
`therefore (1)/(v) = -(1)/(f) +(1)/(u) = -(1)/(f) -(1)/(mf)`
`= -(1)/(f) (1+(1)/(m))= -(1)/(f)((m+1)/(m)) =(m+1)/(-mf)`
`therefore (1)/(v) =(m+1)/(u) ( because u= -mf)`
`therefore ` Linear magnification `=(v)/(u) =(1)/(m+1)`