When the difference between the paths of the marginal waves is _half a
wave-length,_ a partial destruction of the light is effected. The
luminous intensity corresponding to this obliquity is a little less
than one-half--accurately 0.4--that of the undiffracted light. If the
paths of the marginal waves be three semi-undulations different from
each other, and if the whole beam be divided into three equal parts,
two of these parts will, for the reasons just given, completely
neutralize each other, the third only being effective. Corresponding,
therefore, to an obliquity which produces a difference of three
semi-undulations in the marginal waves, we have a luminous band, but
one of considerably less intensity than the undiffracted central band.

With a marginal difference of path of four semi-undulations we have a
second extinction of the entire beam, because here the beam can be
divided into four equal parts, every two of which quench each other.
A second space of absolute darkness will therefore correspond to the
obliquity producing this difference. In this way we might proceed
further, the general result being that, whenever the direction of
wave-motion is such as to produce a marginal difference of path of an
_even_ number of semi-undulations, we have complete extinction; while,
when the marginal difference is an _odd_ number of semi-undulations,
we have only partial extinction, a portion of the beam remaining as a
luminous band.

A moment's reflection will make it plain that the wider the slit the
less will be the obliquity of direction needed to produce the
necessary difference of path. With a wide slit, therefore, the bands,
as observed, will be closer together than with a narrow one. It is
also plain that the shorter the wave, the less will be the obliquity
required to produce the necessary retardation. The maxima and minima