# Lamp height above the street

**1. The problem statement, all variables and given/known data**

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?

**2. Relevant equations**

**3. 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: Lets 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?

http://ift.tt/O26lsR

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