The right model for shading in Ray tracing?

Well, no, light shouldn't be averaged. Think about it. If you have just one powerful light source, and you add another, very faint light, would the color of the object be diminished?

For example say the powerful light has intensity 10, the color (presuming the direction is perpendicular to the normal, and no ambient light, for simplicity sake) would be 10. Then after you add the second faint light, with say intensity 0.1 the color would be (10 + 0.1) / 2 which is 5.05. So adding more light would make the object seem darker. That doesn't make sense.

1 Taken to the extreme, if you have an infinite number of lights you would have zero net light if you averaged it. Lights are independent of each other. – Ron Warholic Jan 3 at 17:25.

In the real world, light adds. It should in your ray tracer, too.

Luminance is not a linear function of light intensity. In other words, two identical light sources aimed at one spot are not perceived as twice as "bright" as one light. (Brightness is an ambiguous term -- luminance is a better term that means radiance weighted by human vision).

What you can do as an approximation to correcting the image to be viewed on your monitor, knowing intensities of various pixels, is called gamma correction.

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