Lord Rayleigh's Investigations in Optics. 49 



which would be that of an actual ray if the refractive index 



cos 6' 



were changed from a to a- 7i . Since sin ^ / = /*~ 1 sin 6, 



& V 'cos (9 r ' 



and 6, 6 f are supposed to be small, the virtual change in the 

 refractive index is from //, to /ul + \ (fjL—fjb~ 1 )6 2 . Thus, if 8/j, re- 

 present the range of refrangibilities confused in the resulting 

 spectrum of an infinitely thin slit, 



S/^^-iy (44) 



The factor /n—fj,' 1 is equal to unity when /^ = 1*62, and for 

 glass will never differ much from unity. By comparison with 

 (31), it would appear that in the case of a 60° prism in the 

 position of minimum deviation, the admissible vertical angular 

 aperture is twice as great as the admissible horizontal angular 

 aperture ; but, on account of the variable distribution of light 

 in the image, this conclusion probably requires modification 

 in favour of the horizontal aperture. 



If there is to be no confusion of the two soda-lines when 

 seen with a prism of extra-dense glass one inch high, the dis- 

 tance of the radiant points must exceed four feet. 



Equation (44) is applicable without change to a spectroscope 

 of any number of properly adjusted prisms of similar material. 



§ 8. The Design of Spectroscopes. 



The circumstances under which spectroscopes are used 

 are so various that it is probably impossible to lay down 

 any one construction as absolutely the best; but the princi- 

 ples of the foregoing sections allow us to impose certain limi- 

 tations within which the choice of the designer must be con- 

 fined. The first point to be considered is the resolving-power. 

 This, in the case of prismatic instruments of one given mate- 

 rial, carries with it the total thickness traversed; and the 

 question is simply in what form it is most advantageous to 

 employ this thickness. The other points to be attended to are 

 principally illumination, quantity of material, ready applica- 

 bility to various parts of the spectrum, simplicity and ease of 

 construction. 



To a certain extent the requirements of illumination and re- 

 solving-power are antagonistic. If, indeed, the eye were a 

 perfect instrument, a beam of diameter equal to that of the 

 pupil would present the full degree of brightness, and a resol- 

 ving-power corresponding to the thickness employed. But, 

 as was explained in § 3 (vol. viii. p. 272), in order to obtain the 

 full value of the thickness it is necessary further to narrow the 



Phil. Mag. S. 5. Vol. 9. No. 53. Jan. 1880. E 



