Rates of Change

[teej047]

If f'' is the focal length of a convex lens and an object is placed at a distance 'p' from the lens, then its image will be at a distance 'q' from the lends, where 'f', 'p', and 'q' are related by the lens equation 1/f = 1/p + 1/q. Find the rate of change of 'p' with respect to 'q'.

I don't even know where to begin with this problem. Any help would be greatly appreciated![/i]

 

[galactus]

There are no particular rates given, so I reckon just the general dp/dt.

\(\displaystyle \L\\\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\)

Differentiate:

\(\displaystyle \L\\\frac{-1}{p^{2}}\cdot\frac{dp}{dt}-\frac{1}{q^{2}}\cdot\frac{dq}{dt}=0\)

\(\displaystyle \L\\\frac{dp}{dt}=\frac{-p^{2}}{q^{2}}\cdot\frac{dq}{dt}\)