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Not so well known is the ratio of reflected up-light to direct up-light from the

You can always contact me if you find a problem with the following.

The luminous intensity of an ideal point source of light can be expressed in terms of its luminous flux (lumens) by

All of the light from a "simple" full-cutoff luminaire, with a perfect internal reflector but no direction of the light, is shed into just one hemisphere. Here ω = 2π, and I = F/2π.

The illumination on a flat surface is related to the intensity of the light source through the cosine law, E = I/D

The radius r is D in our diagram on the previous page and varies by H/cosΘ, so that r

Expressed by the luminous (lumen) output, the illumination

The total illumination the ground sees will be found by the area under cosΘ rotated about the E axis for our function; (the volume of cosΘ about the y axis).

Total illumination E is the

Using the shell method with incremental area dA taken parallel to the y axis:

The volume V = (Length)(Height)(Width), which are: 2πx, f(x), and the increment is dx, respectively. Integrating then...

Therefore, expressed in terms of the lumen output of an ideal point source of light with r (or D in this diagram) being the linear distance from the source to the ground, the total illumination the ground receives (sees, not reflects) is

Yes, there's always a correction factor of 0.571x for the reflected light from an ideal source (and ideal Lambertian flat surface), and a 1x correction factor for any direct light shining from the fixture into the sky. Summarizing...

For a full-cutoff fixture only a

That "ρ" is actually the Greek Rho (ρ) and it's the coefficient of reflectivity. I measured the average reflectivity for aged but dry asphalt to be at ≈ 13%.

Putting in some values for the light-balance of a classic cobra-head having some up-light by direct and reflected light, we can estimate the total up-light.

Things are just a little more complicated than this "ideal" light source or "Lambertian" surface. More details can be found in "

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