1877.] 



Magnifying -power of the Half-prism, 



9 



angle between the pencils coming from the two edges of the slit will, for 

 any monochromatic light, also be increased in nearly the same ratio, and 

 thus the lines in any spectrum become broader as they are further sepa- 

 rated by virtue of this property, and the purity of the spectrum remains 

 unaltered. In fact the half -prism is from this point of view equivalent 

 to a cylindrical magnifier, a property which may prove most useful in 

 the construction of the spectroscope, leading to the substitution of three 

 or, at the most, four half -prisms for the long -train of fifteen or twenty 

 isosceles prisms now used. Eor this purpose direct-vision prisms will 

 be most suitable; but I propose to begin by considering the simpler 

 case of a half -prism of flint. The expression " Magnifying-power " may 

 be conveniently extended to the property in question, which, as will be 

 seen presently, is strictly analogous to that of a lens ; for it will be found 

 that the same law holds with combinations of prisms as with other optical 

 combinations, viz. the magnifying-power is the ratio of the breadth of 

 the incident to the breadth of the emergent pencil*. 



In consequence of the property of the half -prism stated above, it becomes 

 necessary to distinguish between separation accompanied by increased 

 breadth of the lines and separation in terms of this breadth. If the sense 

 of the term " dispersion" had not been fixed by usage, it might very well be 

 applied to the latter effect, retaining " separation " for the other ; but it 

 will undoubtedly be more in conformity with received ideas to define 

 " dispersion w as the angular length of the spectrum, whilst the term 

 " purity " may be used for the ratio of this angular length to the angular 

 breadth of the spectrum lines (expressed in terms of the angular width of 

 the slit). In the case of an isosceles prism, for which the magnifying- 

 power is 1, the dispersion and purity are equal. 



I will therefore distinguish the two positions in which a half-prism can 

 be placed with respect to the incident rays as " Magnifying" and " Dimi- 

 nishing," according as the perpendicular face is turned towards the slit 

 or away from it. It will be found that the first position will be suitable 

 in cases where wide separation of the lines is required, and the second 

 where great purity in the spectrum is of importance ; but before entering 

 on this point and on the further comparison with the ordinary combina- 

 tions of isosceles prisms, it is desirable to find a convenient expression for 

 the dispersion in different cases, con fin ing this term to the effect of the 

 variation in the refractive index. 



* This law follows at once from the principle of conservation of energy, since the 

 total energy of all the pencils which pass through the slit and fall (in a state of paral- 

 lelism) on the prism is measured by the product of the breadth of the pencil into the 

 angular width of the slit. If, therefore, by the refraction at any surface the breadth of 

 the pencil is diminished, the angular breadth of the monochromatic image of the slit 

 must be increased, the narrower pencils being spread oyer a larger angle, since the 

 total energy remains constant. This is of course the ordinary law of brightness of 

 optical images ; a more formal proof from purely geometrical considerations is given 

 in the text. 



