The coincidence of the various bright bands occurs when this quantity is as independent as possible of λ, that is, when n is the nearest integer to
| n = − | b | dv | |
| D | dλ |
(1);
or, as Airy expresses it in terms of the width of a band (Λ), n = −dv/dΛ.
The apparent displacement of the white band is thus not v simply, but
v − Λdv / dΛ
(2).
The signs of dv and dΛ being opposite, the abnormal displacement is in addition to the normal effect of the prism. But, since dv/dΛ, or dv/dλ, is not constant, the achromatism of the white band is less perfect than when no prism is used.
If a grating were substituted for the prism, v would vary as Λ, and (2) would vanish, so that in all orders of spectra the white band would be seen undisplaced.
In optical experiments two trains of waves can interfere only when they have their origin in the same source. Otherwise, as it is usually put, there can be no permanent phase-relation, and therefore no regular interference. It should be understood, however, that this is only because trains of optical waves are never absolutely homogeneous. A really homogeneous train could maintain a permanent phase-relation with another such train, and, it may be added, would of necessity be polarized in its character. The peculiarities of polarized light with respect to interference are treated under [Polarization of Light].