Now in the integrals represented by G and H every element diminishes as V increases from zero. Hence, as CA increases, viz. as the point P is more and more deeply immersed in the shadow, the illumination continuously decreases, and that without limit. It has long been known from observation that there are no bands on the interior side of the shadow of the edge.
The law of diminution when V is moderately large is easily expressed with the aid of the series (16), (17) for G, H. We have ultimately G = 0, H = (πV)−1, so that
I² = 1/π²V²,
or the illumination is inversely as the square of the distance from the shadow of the edge.
For a point Q outside the shadow the integration extends over more than half the primary wave. The intensity may be expressed by
I² = (½ + Cv)² + (½ + Sv)² (22);
and the maxima and minima occur when
| (½ + Cv) | dC | + (½ + Sv) | dS | = 0, |
| dV | dV |
whence
sin ½πV² + cos ½πV² = G (23).