ose waves which diverge laterally behind the
second slit. In this case the waves from the two sides of the slit
have, in order to converge upon the retina, to pass over unequal
distances. Let A P (fig. 19) represent, as before, the width of the
second slit. We have now to consider the action of the various parts
of the wave A P upon a point R' of the retina, not situated in the
line joining the two slits.

[Illustration: Fig. 19.]

Let us take the particular case in which the difference of path from
the two marginal points A, P, to the retina is a whole wave-length of
the red light; how must this difference affect the final illumination
of the retina?

Let us fix our attention upon the particular oblique line that passes
through the _centre_ O of the slit to the retina at R'. The difference
of path between the waves which pass along this line and those from
the two margins is, in the case here supposed, half a wavelength. Make
_e_ R' equal to P R', join P and _e_, and draw O _d_ parallel to P e.
A e is then the length of a wave of light, while A _d_ is half a
wave-length. Now the least reflection will make it clear that not only
is there discordance between the central and marginal waves, but that
every line of waves such as _x_ R', on the one side of O R', finds a
line _x_' R' upon the other side of O R', from which its path differs
by half an undulation--with which, therefore, it is in complete
discordance. The consequence is, that the light on the one side of the
central line will completely abolish the light on the other side of
that line, absolute darkness being the result of their coalescence.
The first dark interval of our series of bands is thus accounted for.
It is produced by an obliquity of direction which causes the paths of
the marginal waves to be _a whole wave-length_ different from each
other.

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