

&m^^ 



A NOTE ON THE MEASUREMENT OF THE VERTlOAL 

 DIMENSIONS OF OBJECTS BY THE USE OF THE 

 GRADUATED FBNE ADJUSTMENT. 



By F. Addey, B.Sc. 



(Read October Uth, 1921.) 



Figs. 1-5 m Text. 



The difference between the readings with two settings of the fine 

 adjustment gives the distance through which the microscope has 

 been moved to or from the object. If the microscope be first 

 focused on the lower surface of the object, and then on its upper 

 surface, the distance through which the microscope has been 

 moved will be equal to the actual depth between the surfaces, if 

 the object be in air. But if the object be immersed in a medium 

 of which the refractive index is different from unity, the apparent 

 depth, as given by the readings of the fine adjustment, will not 

 be the true depth. The correction which has to be applied to the 

 apparent depth to obtain the true depth can be found as follows : 



Consider first a cell of depth t completely filled with a medium 

 of refractive index n (Fig. 1). The rays of light from a point P at 

 the bottom of the cell are refracted at the surface as shown in the 

 diagram for one ray PQR. Let the angles which the ray makes 

 with the normal to the surface, in the medium and in the air, at 

 the point where it emerges, be O^ and 02 respectively. 



Then if we consider a fairly narrow cone of rays, such as we 

 should be concerned with in microscopy, we have : 



1 sin 6-, tan $■, ,, ^.i, i m d/t ^' 



- = _ 1 = -1 (because the angles are small), = -^— = -. 



n sin 2 tan u^ djt t 



Therefore t' = -, or the rays of light from the point P appear 

 n 



to be coming from a point P^, situated at a distance below the 



surface of the medium only -th of the actual depth of the cell. 



n 



If, therefore, we endeavoured to measure the depth of the cell 

 by first focusing on the surface of the medium, and then on the 

 JouRN. Q. M. C, Series II.— No. 88. 20 



