578 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



the dotted line X Y represents the optical or crystallographic 

 axis of the spar, inclined obliquely to the plane of the film of balsam. 

 Following out Ampere's modilication of Huygens's construction 

 for the wave-surfaces, the smaller circle represents the wave-surface 

 of ordinary rays (with which we are not dealing here), and the ellipse 

 the wave-surface (much exaggerated in ellipticity) of extraordinary 

 rays. The wave-surface of the ray in the balsam film will be then 

 represented by the dotted circle whose radius has a certain value 



Fig. 111. 



Fig. 112. 



intermediate between the major and minor semi-axes of the ellipse. 

 Suppose a ray 1, 1', to strike through the sj^ar obliquely upon the film, 

 its path will be found by producing it till it cuts the further side of 

 the ellipse ; there di-awing a tangent to the ellipse meeting the 

 bounding surface at B\ and thence drawing a tangent to the dotted 

 circle, giving as a radius through the point of contact the direction 

 marked 1", which is the direction of this ray through the film. This 

 may be taken as the typical case of all the rays in the useful polarized 

 field of the Nicol. But now consider another ray 2, 2', which 

 traverses the spar in a direction making a greater angle of incidence 

 with the film. A tangent drawn at its jioint of emergence from the 

 ellipse meets the limiting sui-face at B-, icldch falls inside the dotted 

 circle. In this case it is impossible to di-aw a tangent back to the 

 dotted cii'cle : signifying that total reflection takes place internally. 

 Eays then whose directions through the spar are at very small angles 

 with the balsam film, are in the ordinary Nicol cut otf totally, and 

 the limit of their transmission is in the ordinary Nicol marked by the 

 well-known blue band. 



Fig. 112 shows the wave-surfaces in the new prism, the ellipsoid 

 here appearing as a cii'cle whose radius is equal to the semi-major 

 axis of the ellipse of fig. Ill, since the optical axis is in this case in 

 the plane of the film and at right angles to the longitudinal axis 

 of the prism. Take, as before, a ray of 1, 1', draw a tangent at the 

 point of emergence, meeting the plane of the balsam surface at B', 

 the tangent drawn from B' back to the dotted circle gives the 

 direction 1", of the transmitted ray ; and since it is obvious that in 

 no case can the point B^ at any incidence fall within the outer circle, 

 much less within the dotted circle, it is clear that in all cases, and at 

 every incidence, the extraordinary ray is transmitted. Hence the 

 greater ^vidth of the field. 



