# Thread: If f is the focal length of a convex lens and an object is placed at a distance...

1. ## If f is the focal length of a convex lens and an object is placed at a distance...

Been trying to relate this as f is constant, help?

2. ## Re: If f is the focal length of a convex lens and an object is placed at a distance..

We are given:

$\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Treating $\displaystyle f$ as a constant, can you implicitly differentiate with respect to $\displaystyle u$?

3. ## Re: If f is the focal length of a convex lens and an object is placed at a distance..

Write this as $\displaystyle f^{-1}= u^{-1}+ v^{-1}$ and differentiate with respect to u.

$\displaystyle 0= -u^{-2}- v^{-2}\frac{dv}{du}$
$\displaystyle v^{-2}\frac{dv}{du}= -u^{-2}$
$\displaystyle \frac{dv}{du}= -u^{-2}v^2$
$\displaystyle \frac{dv}{du}= -\frac{v^2}{u^2}$.