532 merwin: measurement of refractive index 



sin2/3 



■^ 



sin2/3 



0)2 



CO ^^ _ / 9 . sin'^ 13 



= lj 6^ - sin^ 



sm^ /3 



7\\2 . 2/X 



e2 = co^ + ( — j + ^-- Vco' - sin2 ^ (3) 



A simpler equation than (3), which for such angles as are 

 measurable by the microscope contains an entirely negligible 

 error not greater than 2 or 3 units in the 5th decimal place, is 

 derived as follows: assume that the cosine of the very small 

 angle (ai — a) equals 1, then in (1) m = mi, and in (2) 



«e , eie ZXcosa ZX L sin^ iS .„ s 

 ± I = — - — or ei = CO ± = ,0 ± — * 1 - ^i^i-^ (3a) 



X cos a X cos a 6 e ^ (^^ 



Equation (3) gives exactly, and equation (3a) almost exactly 

 the refractive index of the extraordinary wave whose normal 

 makes with the optic axis the angle aj within the crystal, and the 

 angle j8 in the air. 



From the general equation of the index ellipsoid 



CO sin /3 

 CO sin ai Ci 



I J" , 1 U2 / sin2/3 



e = 



(4) 



Vco2 - ef + sin2 (3 



Substituting! (3) 



r, , ■ ■ \ " sin (8 ,„ > 



ivSubstitutme (3a) we havee= — ,-^- 1 ^ • (oa; 



I , / ^^ sin2^\2 , . ,, 



This value of «, though not precisely correct, has no measurable error. 



