1877.] 



Magnifying -power of the Half-prism. 



21 



prism, we may take as a particular case a = 56°, and /3=106° 32' for the 

 first, and 37° 38' for the second, so that the extreme angle of incidence 

 or emergence at the crown will be the same in both forms, viz. 65° 21'. 

 "We thus have 



Direct-v ision Ha If-p rism . 



Compound Half-prism. 



a =56 0=106 32 



a=56 



:37 38 



Xa 

 Xh 



= 65 21 

 = 55 11 



X A 

 X h 



= 52 56 

 = 65 21 



Dispersion =12 25 



Dispersion =10 10 

 Deviation 



for A= -14 49, for A= +34 34, 



forH=- 4 39, forH=+46 59, 



the deviation being considered positive when it is in the same direction 



as that of the flint prism. 



Magnifying-power. 



m A =3-07 

 w H =3-04 



Irrationality of Dispersion. 



2xa=-t^ (31-8 -4-4) 



150 

 •183 or 



w A =2-26 

 m H =3-96 



^="IoO (23 ' 4 + 2 ' 6) 



10°26' 



*Xh=-^- (31-5-2-9) 

 = -•191 or -10° 57 



r Xn = 



150 



(41-0 + 4-4) 



= -•303 or -17° 22' 



Light lost by Reflexion. 





Polarized 



Total. 



Polarized 



Total. 



in plane 

 of inci- 

 dence. 



in perpen- 

 dicular 

 plane. 



j in plane 

 of incid- 

 ence. 



in perpen- 

 dicular 

 plane. 



Eor A 

 For H 



per cent. 

 36-5 



34-7 



per cent. 

 11-3 



15-3 



per cent. 

 23-9 



25-0 



per cent. 



1 27-1 

 44-1 



per cent. 

 10-4 



15-6 



per cent. 



18-8 

 29-9 



The advantage of the direct-vision prism is thus clearly shown, whether 

 as compared with a compound prism of the other form, or with two 

 simple prisms of the same kind of flint and giving the same dispersion. 



In fact the direct-vision half-prism here considered gives nearly the 

 same dispersion as a simple prism of 64°, with less loss of light and 

 without the great irrationality which makes the dispersion in the other 

 case merely illusory. 



It is to be remarked that there still remains the irrationality in the 

 variation of the refractive index for glass, which may, however, be par- 



