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

Options

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

Answer

A

Explanation

`1/v-1/(-u)=1/f , u/v + 1 = u/f`
`(1/m + 1)=u/f , ((m+1))/m=u/f`
Also, u+v=x
`1+v/u=x/u , (1+m)=x/u`
Multiplying equations. (i) and (ii),
`((m+1)^2)/m =x/f , f=(mx)/((m+1)^2)`