A convex lens of focal length `f` produces a virtual image `n` times the size of the object. Then the distance of the object from the lens is

Options

A. `v=f(m-1)`
B. `v=f(1-m)`
C. `v=(f)/(m+1)`
D. `v=f(m+1)`

Answer

D

Explanation

`M=(I)/(o)=(v)/(u)=m therefore v=m u therefore u=(v)/(m)`
`because (1)/(v)-(1)/(u)=(1)/(f)`
For the convex lens, u = -ve
`therefore (1)/(v) -(1)/((-(v)/(m)))=(1)/(f) therefore (1)/(v)+(m)/(v)=(1)/(f)`
`therefore (1+m)/(v) =(1)/(f) therefore v=f(m+1)`