(16).
The ratio λ/λ′ is thus determined as a function of the angular diameters x, x′ and of the integers P, P′. If P, say for the cadmium red line, is known, an approximate value of λ/λ′ will usually suffice to determine what integral value must be assigned to P′, and thence by (16) to allow of the calculation of the corrected ratio λ′/λ.
In order to find P we may employ a modified form of (16), viz.,
| P′ | = | λ | ( 1 + | x2 | − | x′2 | ) |
| P | λ′ | 8 | 8 |
(17),
using spectrum lines, such as the cadmium red and the cadmium green, for which the relative wave-lengths are already known with accuracy from A. A. Michelson’s work. To test a proposed integral value of P (cadmium red), we calculate P′ (cadmium green) from (17), using the observed values of x, x′. If the result deviates from an integer by more than a small amount (depending upon the accuracy of the observations), the proposed value of P is to be rejected. In this way by a process of exclusion the true value is ultimately arrived at (Rayleigh, Phil. Mag., 1906, 685). It appears that by Fabry and Pérot’s method comparisons of wave-lengths may be made accurate to about one-millionth part; but it is necessary to take account of the circumstance that the effective thickness t of the plate is not exactly the same for various wave-lengths as assumed in (16).
§ 9. Newton’s Diffusion Rings.—In the fourth part of the second book of his Opticks Newton investigates another series of rings, usually (though not very appropriately) known as the colours of thick plates. The fundamental experiment is as follows. At the centre of curvature of a concave looking-glass, quicksilvered behind, is placed an opaque card, perforated by a small hole through which sunlight is admitted. The main body of the light returns through the aperture; but a series of concentric rings are seen upon the card, the formation of which was proved by Newton to require the co-operation of the two surfaces of the mirror. Thus the diameters of the rings depend upon the thickness of the glass, and none are formed when the glass is replaced by a metallic speculum. The brilliancy of the rings depends upon imperfect polish of the anterior surface of the glass, and may be augmented by a coat of diluted milk, a device used by Michel Ferdinand, duc de Chaulnes. The rings may also be well observed without a screen in the manner recommended by Stokes. For this purpose all that is required is to place a small flame at the centre of curvature of the prepared glass, so as to coincide with its image. The rings are then seen surrounding the flame and occupying a definite position in space.
The explanation of the rings, suggested by Young, and developed by Herschel, refers them to interference between one portion of light scattered or diffracted by a particle of dust, and then regularly refracted and reflected, and another portion first regularly refracted and reflected and then diffracted at emergence by the same particle. It has been shown by Stokes (Camb. Trans., 1851, 9, p. 147) that no regular interference is to be expected between portions of light diffracted by different particles of dust.
In the memoir of Stokes will be found a very complete discussion of the whole subject, and to this the reader must be referred who desires a fuller knowledge. Our limits will not allow us to do more than touch upon one or two points. The condition of fixity of the rings when observed in air, and of distinctness when a screen is used, is that the systems due to all parts of the diffusing surface should coincide; and it is fulfilled only when, as in Newton’s experiments, the source and screen are in the plane passing through the centre of curvature of the glass.
| Fig. 5. |