THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] ^>* 



W 



M 1* 





^ F 1897. V^S, PATEH^i 





XLV. O/i the Resolving Power of Telescopes and Spectroscopes 

 for Lines of Finite Width. By F. L. 0. Wadsworth *. 



THE question of the theoretical resolving power of optical 

 instruments has been discussed by a number of writers — 

 most fully and comprehensively by Rayleigh f, who has shown 

 that the theoretical angular resolving power of any instru- 

 ment having an aperture of width b is a, =my, where a is the 



angle between two fine lines or points which can just be 

 separated (two stars for example), X is the mean wave-length 

 of light, b the linear aperture of the instrument, and m a 

 constant varying from unity for a rectangular aperture to 

 about 1*1 for a circular aperture. It is possible to determine 

 at once from this expression the spectral resolution or 

 separation of a spectroscope, by remembering that the 

 function of the dispersing train, which may consist either of 

 prisms or of a transmission or reflection grating, is simply to 

 form a series of spectral images of a single source, — the slit 

 of the spectroscope. Of these images only those will be 

 resolved or separated for which the difference in angular 

 dispersion is equal to or exceeds the angular resolution a. of 

 the spectroscope aperture. In the case of the spectral images 



* Communicated by Lord Rayleigh, F.R.S. 



t " Resolving or Separating Power of Optical Instruments," Phil. 

 Mag. Oct. 1879, p. 261. " Resolving Power of Telescopes," Phil. Mag. 

 Aug. 1880. " The Manufacture and Theory of Diffraction Gratings," 

 Phil. Mag. 1874, p. 5. Also articles on Optics, vol. xvii., and Wave 

 Theory, vol. xxiv. JEnc. Brit. 



Phil. Mag. S. 5. Vol. 43. No. 264. May 1897. 2 



