OBJECTS BY USE OF GRADUATED FINE ADJUSTMENT. 281 



to the top and bottom of the body, and the apparent distances as 

 measured by the fine adjustment be t\ and t'2, respectively, then 

 we shall have 



and t-y = nt\. 



Therefore t^ ~t-^ = n {i\ — i'^. 



Now the true thickness, %, of the body, is ^2 — ^i- 



Therefore h = n {t\ — t'-^, or the apparent thickness of the body 

 immersed in a medium of refractive index n, has to be multiplied 

 by n to obtain the true thickness. 



In the cases we have just considered, the surface of the medium 

 has been assumed to be in direct contact with the air. We have 

 now to enquire what effect is produced when a cover glass is 

 present between the medium and the air. 



Consider first the apparent depth of a cell filled with a medium 

 of refractive index n-y and provided with a cover glass of refractive 

 index n^. Assuming that n^ is greater than Wj^ the path of a ray 

 from a point P on the bottom of the cell will be as shown in Fig. 3, 

 and the ray when it emerges into the air will appear to come from 

 a point Pj raised above the bottom of the cell. 



If the refractive index of the medium be greater than that of the 

 cover glass, the ray on passing from medium to glass will be bent 

 the other way, but the only result of this will be that the point P^ 

 will be raised further above the bottom of the cell than it is 

 when the refractive index of the cover glass is the gxeater. The 

 mathematics will be exactly the same in both cases. 



Let us take first the refraction from medium to cover glass. 

 We have : 



Wo sin ^] tan 6-, ,-, , i i _ ii\ dJU t\ 



-^ — - — ^ ■=■ -^ (because the angles are small), = -^- = -^. 



% sm ^2 tan B^^ ^ d^lt\ t^ 



Therefore t\ = ^ - L. 



Take now the refraction from cover glass to air. We have : 



1 = s^^^g =, tan ^2 ^ ^zlik + ^'i) _ k + t'\ 

 n^ sin ^3 tan 0^ djih + ^"i) k + ^'i' 



But t\ = ^-^ ' L. 



