- #1
skrat
- 748
- 8
Homework Statement
Above the center of the street a lamp is hanged. A lamp radiates equally in all directions. How high does the lamp have to be so the edge of the road is as bright as possible?
Homework Equations
The Attempt at a Solution
I'm kinda lost here...
##j=\frac{P}{A}## where ##A=4\pi r^2## therefore
##j=\frac{P}{4\pi r^2}##.
Now the idea is to get ##j(h)## but nothing seems to work... For example: Let's say that the street is ##2a## wide, therefore ##r^2=h^2+a^2##.
##j=\frac{P}{4\pi (h^2+a^2)}##
##\frac{\partial j}{\partial h}=-\frac{P}{4\pi}\frac{2h}{(h^2+a^2)^2}=0##...
Hmm, what am I missing here?