Here are a series of 10 stacked planes, each of different length, so that we have regions where we look through 1 plane, then 2, then 3, and so on.

Each plane removes some of the light passing through. Let's let T represent the transparency, or the fraction of light that can pass through.

The luminance through one layer is T times the object behind the layer, my checkerboard.

The second does the same, taking what comes in and letting T of that through. So the 2nd layer passes T * T of the light.

The third layer passes T * T * T.

It should be apparent that the Nth layer passes T ** N of the light through.

Now when we model a volume of translucent material with sheets like this, we're letting each sheet represent a slice of the volume. The more of these we use to model the volume, the more transparent each sheet needs to be. Using calculus, if we take the limit as the number of sheets approaches infinity, and the thickness of each slice approaches 0, it exactly models a volume. And in that limit, the effective transparency is T ** D, where D is the distance that the light has to pass through.

If the distance is infinitely long then the amount of light passing through is T to the infinite power, which is 0. But for any distance that is not infinite, then the transparency is greater than 0. So this is interesting. A translucent material of finite thickness cannot block all the light. There is always some non-zero amount that can get through. 

---

Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)