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 length of the lens is

Step-by-step solution

Given, distance between object and screen for convex lens =x i.c u+v=x but magnification, m= v u From Eqs. (i) and (ii), we get array rlrl & & u+m u & =x u(m+1)=x & u & = x m+1 array Again from Eqs. (i) and (ii), we get aligned v m +v & =x v ( 1 m +1 )=x & = m x m+1 aligned Using lens formula , 1 f = 1 v - 1 u = 1 ( m x m+1 ) - 1 ( -x m+1 ) [from Eqs. (iii) and (iv)] aligned & = m+1 m x + m+1 x = m+1 x [ 1 m +1 ] & = m+1 x ( 1+m m )= (m+1)^2 m x f= m x (m+1)^2 aligned