# distance help

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• Oct 25th 2009, 11:15 AM
friday616
distance help
Let a and d be positive numbers. Suppose that two light sources are separated by a distance d and that one source is a times as bright as the other. Find the point between the light sources at which there is the least amount of light. Use the fact that the intensity of the light at a point is proportional to the reciprocal of the square of the distance from the light source.
• Oct 25th 2009, 11:43 AM
skeeter
Quote:

Originally Posted by friday616
Let a and d be positive numbers. Suppose that two light sources are separated by a distance d and that one source is a times as bright as the other. Find the point between the light sources at which there is the least amount of light. Use the fact that the intensity of the light at a point is proportional to the reciprocal of the square of the distance from the light source.

$I = \frac{k}{r^2}$

at a point between the two sources a distance $r < d$ from the $a$ factor source ...

$I = \frac{ka}{r^2} + \frac{k}{(d-r)^2}$

find $\frac{dI}{dr}$ and minimize