can someone help me to create an equation to model a situation?

Question

To illuminate a field you are given a lamp with an intensity of 90w/m^2. The distance is 5m. Write an equation to model the situation and then solve or the constant of variation. If you can't answer, some help understanding what the question asks would be helpful.

Answer 1

First you need to assume something about the source. Let's assume it's a point source emitting into $4\pi$ steradians. So the power (i.e., $\text{W/m}^2$) will fall off as $1/r^2$, if I recall correctly. Now you have to say something about the target besides the distance. Is it for example a circular disk? An infinite wall? What? Then you need to specify what you want to know about the target, for example, the irradiance (also $\text{W/m}^2$). To get that you'll have to integrate the radiant intensity ($\text{W/m}^2/\text{sr}$) over the target. Basically, you've provided a rather incomplete description of the problem you need to solve.