A convex lens of focal length `f` is placed somewhere in between an object and a screen. The distance between the object and the screen is `x`. If the numerical value of the magnification produced by the lens is `m`, then the focal lnegth oof the lens is .

Options

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

Answer

A

Explanation

`- m = (v)/(-u) and v + u = x `
`rArr u + mu = x rArr u = (x)/(1+ m )`
`(1)/(f) = (1)/(v) - (1)/(u)`
`rArr f = (uv )/(u - v) = (mx)/((m + 1)^(2))`.