66 THEOEY OF THE MICROSCOPE. 



If a b (Fig. 26) is an incident ray which passes through the 

 Cover-glass in the direction b c and then passes into the original 

 medium, c s is parallel to a b. The position of the point a, in 

 which the emergent ray, produced backwards, cuts the per- 

 pendicular a p, can therefore be trigonometrically determined. 

 Then, if a is the angle of incidence, a the angle of refraction, 

 and D the thickness of the cover-glass, we get in the first place 



be = -. . The triangle q c b gives, therefore, 



cos a 



_ sin (a a) 

 qc = be. - -. 



cos a 



Since a' c is parallel to a q, we obtain from the triangle a q p 



oaf : qc = ap : pq = cos a : sin a ; 



consequently 



cos a 



aa = qc. 



sin a 



If we substitute for q c and b c their values, we get 



n sin ( a - g/ ) 

 aa = JJ 7 



sin a cos a 

 and, by an evident reduction, 



, / tan a 



aa = D (I , 



\ tan a 



If a is taken as 40, and the refractive index of the cover-glass 

 1*5, then, if the surrounding medium is water, we get 



aa' = '168106 X D, 

 and if the surrounding medium is air, 



aa' = -565037 x D. 



In the most usual case (i.e., water below, air above) the latter 

 expression is increased to a small extent, varying with the 

 distance of the object-point from the lower surface of the cover- 

 glass, and when the distance = 0, this is also zero. 1 



1 The lateral displacement which takes place when the light is incident 

 obliquely has too little practical interest to require further discussion here. 

 The obliquity of the illumination is entirely without importance, for the 

 contour-image and the delineation of details are dependent upon factors^ 

 unconnected with the path of the rays. Cf. on this point the chapter on the 

 Theory of Microscopic Observation. 



