Has there ever been found a relation between some properties of light (its speed, how mass increases as an object nears light speed, the degree to which light is bent by a gravity field, possible energy levels of photons, etc.) and the equation ? Or rather, are there any phenomena ascribed to light/photons that can be reduced to or is described by the equation? I know this is a pretty vague question, but any answer would be welcome.

The [math]1/r^{2}[/math] law in electromagnetism?

Electromagnetism similar to gravity? Or are they the same law?

They are similar, both have the [math]1/r^{2}[/math] law for example.

They are similar, both have the [math]1/r^{2}[/math] law for example.

Do they now? Thanks, that is what I was looking for. I'll read up on it a bit.

A lot of things have that law - anything that "emanates." If you think about it, it's just a matter of geometry, specifically the equation for the surface area of a sphere, A=4pi(r^2), more specifically the fact that surface area increases with the square of the radius. Think about a light source giving off radiation. Picture a sphere around it with a ten foot radius, then one with a twenty foot radius. Each one intercepts all the light from the source, but the larger one has four times the surface area, and hence 1/4 the intensity per unit area. So intensity varies with the inverse square of the distance from the source.

Electromagnetism similar to gravity? Or are they the same law?

electromagnetism is similar to gravity as they both follow the inverse square law.They are different in other respect as gravity is only attractive and electomagnetism can be attractive and repulsive.