1877.] 



Magnifying -power of the Half -prism. 



15 



1. Isosceles prism of 60°. 



A=8° 4'. Loss of light for H = 25 per cent. 1 

 for A = 20 per cent. J 



Irrationality of dispersion 



2^ A =2m A fyztan f = -135 or 7° 44'. 

 2^ H =2m H S/xtan f,= '153 or 8° 46'. 



2. Isosceles prism of 64°. 



2A = 10° 54'. Loss of light for H=34 per cent, j 



for A =25 per cent. J 



Irrationality of dispersion 



2% =2m A tan if/=\L74 or 9° 58'. 

 2^=2m H fytajiif/ = -218 or 12° 30'. 



In computing the loss of light after passing through several surfaces, 

 the two polarized beams must of course be taken separately and after- 

 wards combined. 



The quantities given under Irrationality of Dispersion represent what 

 ■would be the length of the spectrum if the scale were the same through- 

 out as at A and H respectively. This is independent of irrationality in 

 the refractive index of glass as referred to wave-lengths. 



If we had taken an ordinary flint, the above numbers would be con- 

 siderably modified. Thus taking ^u A = 1*6200, and fx K =l-6666, which 

 correspond to a moderately dense flint, Fraunhofer's No. 30, specific 

 gravity 3*7, we should have 



Tor a prism of 60°, 



i// A =54° 6', ^ H =56° 25', dispersion = 4° 38'. 



Compound Peism. 

 Let j3 be the refracting angle 1 f of the prism of crown glass which is 

 ii the refractive index J \ cemented to the half-prism of flint, 

 X, % t ne angles of emergence and refraction at the outer surface 

 of the crown, 



the other angles being denoted as before, though the relation between 

 \p and \p' will now be 



fx sin \p=fi sin xp'. 



Two cases here present themselves according as (3 is greater or less than \p. 

 The former gives the direct-vision prism, and the latter the compound 

 prism commonly used in large spectroscopes. 



In the first case we have x' — fi-> in the second \p—x'=(3; but this 

 can be reduced to the first case by considering x as negative. In con- 

 formity with this we shall consider the angles of refraction as positive 

 when they fall on the side of the normal towards the edge of the prism 

 (whether flint or crown) in which the refraction takes place, and the 

 angles of incidence or emergence as positive when they fall on the side 

 from the edge. 



