The resolving power of spectrometers under conditions such that the limiting factor is the finite slit widths necessary to obtain the minimum energy required for measurement has been discussed by J. Strong, Phys. Rev. 37, 1661 (1931).
Rayleigh's statement in the Encyclopaedia Britannica, Vol. XXIV (1888), is: "We conclude that a double line cannot be fairly resolved unless its components subtend an angle exceeding that subtended by the wave-length of light at a distance equal to the horizontal aperture." Note that this statement contains no basis for distinguishing between the cases of the absorbing and the non-absorbing prisms.
H. M. Reese, Astrophys. J. 13, 199 (1901).
This is valid for all values of ƒ since, as ƒ→0, r→∞ in such a way that rƒ is finite.
The limiting values given in (7) and (8) are obtained from the equations 6+(r2ƒ2w2-6) cos rƒw-4rƒw sin rƒw = 0 (6a) and 6r2-2 = 0 (6b) to which (6) may be reduced in the limits ƒw→0 and ƒw→∞, respectively. Note that w is finite and » 0 since W»λ.
It is assumed throughout that n, dn/dλ, and k are evaluated at the given wave-length λ.
See, for example, R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), third edition, p. 251.
H. M. Reese (reference 3) discusses in some detail the determination of minima and maxima in I(θ).
In the calculation of λ/Δλ for rocksalt, n and dn/dλ were obtained from the data of F. Paschen [Ann. d. Physik 26, 120 (1908)] as corrected to 25° by P. C. Cross [Rev. Sci. Inst. 4, 197 (1933)]. The values of k were determined from the transmission data of H. Rubens and A. Trowbridge [Ann. d. Physik 60, 724 (1897)].