avright: measurements of refractive indices 535 



recently been shown by H. E. Merwin, of this Laboratory, 

 in the measurement of the refractive indices of minute uniaxial 

 crystal flakes of arsenic iodide; Dr. Merwin measured the angular 

 width of the concentric interference rings and from these computed 

 the refractive index € by means of a formula^ which he found to 

 furnish accurate results for uniaxial sections normal to the axis. 



Derivation of formulae.- For 

 the particular case of principal 

 sections the accurate formulae 

 can be derived directly as fol- 

 lows: Let figure 1 represent a 

 principal section of a birefract- 

 ing plate. Let KC be the inci- 

 dent, plane-polarized beam of 

 light (in air); CA and CB, the 

 two refracted wave normals; 

 AD and BE the two parallel y\^. i 



emergent beams (in air), which 



enter the objective and are brought to focus in its upper focal 

 plane whence they pass through the analyzer to the eye of the 

 observer. For the incident and refracted wave normals the 

 general relations (invariants) obtain 



no sin i = ; 1 sin ri = ^2 sin r2 (1) 



in which i is the angle of incidence; ?'i, the angle of refraction of 

 the faster wave; ro, the angle of refraction of the slower wave; 

 no, the refractive index of air (for present purposes no may be 

 considered = 1); Ui, the refractive index of the faster wave; 

 7i2, the refractive index of the slower wave. The interference 

 phenomena are the result, primarily, of the difference in optical 

 path between the two refracted waves, starting at C and at- 

 taining again a common wave front at BF. This path-difference 

 is expressed by the equation: 



^ = k-\ = n^-CA + 710- AF - nr CB 



1 J. Wash. Acad. Sci., 4: 532, equation (6a). 1914. 



- The derivation of the formulae for the general case of any section of a bire- 

 fracting mineral is given in text books on crystal optics (Pockels, Lehrbuch der 

 Kristalloptik. Chaps. II, IV, IX, 1906). 



