90 



PHOTO-MICROGRAPHY 



their straight inner edges parallel to one another, and a definite distance (say 

 20 centimetres for lenses of N. A. over 0*50, less for low-angled ones) apart, then 

 hold a rule vertically upon the table about midway between the two pieces of paper. 

 Next hold the objective to be tested vertically against the rule and look down at the 

 back lens. Images of the two pieces of paper will be seen there ; now slide the 

 objective downwards along the edge of the rule, always watching these images. 

 They will separate farther and farther apart until at last a point is reached where 

 only a slight bluish flicker remains visible on either side in the extreme margin of the 

 lens, which, of course, indicates that the inner edges of the pieces of paper are in the 

 direction of the most oblique rays which the objective is capable of receiving, or that 

 the angle enclosed between these directions, (which directions intersect in the principal 

 focus of the objective), is the angle of aperture. To determine this angle, read off the 

 distance from the table to the front of the objective, and subtract the working 

 distance of the lens, so as to get the distance from table to focus. Then this distance 

 divided by half the distance between the two pieces of paper is the cotangent of the 

 semi-angle of aperture ; the latter may, therefore, be obtained from a table of trigno- 

 metrical ratios, and the sine of the same angle is the N. A. of the objective. 



Example : 



Distance between the two pieces of paper, 200 mm. 

 Distance of front lens of objective from paper, 33-0 mm. 

 Working distance of objective, o"2 mm. 



33-0— 0-2 328 



.-. = = 0-328 



200/2 100 



0-328 = cotan of angle 71'' -49', as we find from the trigonometrical tables, the sine 

 of which angle = 0-95 = N. A. 



With great care this method will give results accurate to one or two units of the 

 second decimal. In looking at the back of the objective the eye should be placed at a 

 distance about equal to the tube length for which the objective is designed, but the 

 error caused by even considerable deviations from this theoretically required distance 

 is very small."* 



(iii) Eye-pieces.— With respect to eye-pieces or oculars, as they are often called. 



* For this method the author is indebted to Mr. Conrady. 



