Question

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

• A. $\frac{m x}{(m+1)^{2}}$
• B. $\frac{m x}{(m-1)^{2}}$
• C. $\frac{(m+1)^{2}}{m} x$
• D. $\frac{(m-1)^{2}}{m} x$

Answer 1

Answer: (A)

$\frac{v}{-u}=-m$ and $v+u=x $
$\Rightarrow u=\frac{x}{1+m}$
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u} $
$\Rightarrow f=\frac{m x}{(m+1)^{2}}$