Question

A convex lens of focal length $f$ is placed somewhere in between the object and a screen. The distance between object and screen is $x$. If magnification produced is $m$, the focal length of the lens is:

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

Answer 1

Answer: (A)

$\frac{mx}{{(m+1)}^2}$

If we consider that the object is placed at a distance $u$ from the lens, then object distance $=-u$

This gives, $u+v=x$

Also, magnification, $m=$$\frac{-v}{-u}=\frac{v}{u}$

Now, using the lens formula, $\frac{1}{v}-\frac{1}{-u}=\frac{1}{f}$

Solving these 3 equations simultaneously, we get:

$f=\frac{mx}{{(m+1)}^2}$