The equivalent diffracted ray if all were stationary and the wave-length really shortened, θ1.
As an auxiliary we use the aberration angle ε, such that sin ε = α sin θ, where α = v/V.
Among these four angles the following relations hold; so that, given one of them, all are known.
| θ | = φ−ε | |
| sin θ1 | = (1−α) sin θ0 | |
| sin φ | = (1−α vers φ) |
Whence θ and θ1 are very nearly but not absolutely the same. θ1 is the ray observed by an instrument depending primarily on frequency, like a prism; θ is the ray observed by an instrument depending primarily on wave-length, like a grating.
Prism Theory.
Now let a prism be used to analyse the light; its dispersive power is in most theories held to depend directly upon frequency—i.e. upon a time relation between the period of a light vibration and the period of an atomic or electronic revolution or other harmonic excursion.
Let us say, therefore, that prismatic dispersion directly indicates frequency. It cannot depend upon wave-length, for the wave-length inside different substances is different, and though refractive index corresponds to this, dispersive power does not.
In the case of a prism, therefore, no distinction can be drawn between motion of source and motion of receiver; for in both cases the frequency with which the waves are received will be altered,—either because they are really shorter, though arriving at normal speed, or because they are swept up faster, although of normal length.
Achromatic Prism.