282 F. ADDEY ON MEASUREMENT OF VERTICAL DIMENSIONS OF 



Therefore 



1 _ «2 + i"l _ ^2 + fl 



^2 k + «'l t^ 4_ ^^ 



Therefore i? _|_ li _ , .^ ^/' 



or r' =-- li + ^ - L 



= ^ + (i-ik 



% \ »^2/ 



Without the cover glass the apparent depth of the medium 

 would have been -i. Hence the efiect of the cover glass of 

 thickness t^ and refractive index n^ is to diminish the apparent 

 depth by 1 1 — — ^2, and this diminution is independent of the 



depth of the medium. 



Hence the presence of the cover glass has no efiect on the 

 apparent thickness of an object measured in the medium, for the 

 effect which the cover glass exerts in apparently raising the obj ect 

 will be equal on both the top and bottom surface of the object, 

 since it is independent of the depth of the medium, and therefore 

 the apparent distance between these surfaces will not be altered. 



We can express this algebraically as follows (Fig. 4) : 



We have : 



^1 v 



n. 



and t'' =ha-(l -1. 



1 



% \ Wj 



Hence t\i - t'\, = h^ -ha, 



n-i n^ 



Therefore n^ {t\, - t'\,) = ty, — t^^^ h. 



Thus the true thickness of the object is its apparent thickness 

 multiplied by the refractive index of the mounting medium, the cover 

 glass making no difference. 



For water the mean value of the refractive index is 1-336, for 

 Canada balsam the mean value is 1 -540, and for glycerine it is 

 1476. 



