When I use "normal" spot lights as presented in tutorials such as this (with the exception that I use inverse square fall-off and then gamma correction), the spot light doesn't behave like a real spot light would, because in real life I would expect a narrow spot light to cast a brighter light than a broad one. In my primitive understanding this is because the light that would be cast outside of the spot lights casting angle is reflected on the inside of the spotlight device (e.g. flashlight) and effectively cast inside spotlights cone.
The spotlights usually presented in tutorials do not account for this, because the light calculation is still based on a spot light that distributes all of its energy evenly in a 360 degree radius, and the light that isn't visible is simply "clipped away", thus removing energy from the system.
My question is this:
I plan on accounting for this by just multiplying the outgoing color by a factor that depends on the casting angle of the spot light. The function of this factor is just
f(x) = 360/x;
This means that the color will be multiplied by 4 when the spot light casts its light in a 90 degree angle. This function makes the assumption that the energy received by the lit area of a 180 degree spot light is twice as much as the energy received by the lit area of a 360 degree spot light.
Is this assumption correct? If not, how does the energy distribution change with the width of the spot light? Are there maybe other ways to account for this more effectively?