5.6.6 Light Fading

In reality light diminishes with distance, since the number of photons passing through spheres of varying radii centered at the light source is constant, but the surface of the spheres is proportional to the radius squared. So light intensity is inverse proportional to the square of the distance from the source.

By default povray does not take this into account, but by adding the keywords fade_distance D0 and fade_power E one can modify this behavior. The formula for the light intensity reaching an object with distance $D$ from the source with intensity $I$ is given by

$$I\cdot \frac{2}{1+(D/D0)^E}$$

Note that $E=2$ corresponds best to the real situation, but here the term `$1+$' has been inserted in order to avoid ${\infty}$ for $D=0$. The parameter $D0$ is the distance, where this formula gives the prescribed intensity $I$. And for smaller distances the intensity can be as large as $2I$.