GLOBULES OF OIL IN WATER, 



203 



the distribution of light in a given sectional plane to which the 



Microscope is focused, we will again 



apply the principle of the reciprocity 



of the path of the rays, and will pro- 



duce the pencils backwards from the 



objective to any desired points of the 



plane of adjustment, and then trace 



them to the diaphragm. If again a> 



and S are the angles of aperture of 



the objective and of the diaphragm, 



M N (Fig. 110) the plane of adjust- 



ment, and F L a ray directed towards 



the point P, which after two refrac- 



tions proceeds in the direction T S, 



and if, finally, a and a are the angles 



of incidence and refraction ; then the 



half angle of deviation is 



p = %LOT = LOC-, 

 and we get from the right-angled 

 triangle, whose hypotenuse is L 0, the relation 



p = 90 - (a - a'). 



For those points in the plane of adjustment, whose brightness is 

 equal to that of the field of view, the relations and deductions 

 above derived also hold good. 



The constructions there given are applicable here also, if we 

 suppose the cones of rays transposed from the left half of the 

 circle to the right half, so that the points where the refractions 

 take place again fall in the periphery. "We get, therefore, 



and hence, by combination with the above equation, 



a - a 



Similarly, there results for the limiting points, which are illumi 

 nated only by the outermost marginal rays, 



= 90" - 



and consequently 



a a = 



