OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 34, Iss. 9 — Sep. 1, 1944
  • pp: 517–520

Criteria for Resolution and the Resolving Power of Absorbing Prisms

PAUL C. CROSS and EUGENE R. NIXON  »View Author Affiliations

JOSA, Vol. 34, Issue 9, pp. 517-520 (1944)

View Full Text Article

Acrobat PDF (348 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A method is outlined by which the limiting resolving power of any prism may be readily determined. It has been necessary to redefine the limit of resolution as the minimum angular separation of the central maxima of the individual diffraction images at which there may exist a minimum of total intensity between the positions of the individual central maxima. Application to a 10-cm rocksalt prism is included.

PAUL C. CROSS and EUGENE R. NIXON, "Criteria for Resolution and the Resolving Power of Absorbing Prisms," J. Opt. Soc. Am. 34, 517-520 (1944)

Sort:  Author  |  Journal  |  Reset


  1. 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).
  2. 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.
  3. H. M. Reese, Astrophys. J. 13, 199 (1901).
  4. This is valid for all values of ƒ since, as ƒ→0, r→∞ in such a way that rƒ is finite.
  5. 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.
  6. It is assumed throughout that n, dn/dλ, and k are evaluated at the given wave-length λ.
  7. See, for example, R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), third edition, p. 251.
  8. H. M. Reese (reference 3) discusses in some detail the determination of minima and maxima in I(θ).
  9. 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)].

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited