THEORY AND TECHNIQUES 



divider in the condenser system, the numeri- 

 cal aperture of the illuminating bundle is 

 relatively small, about 0.12. 



Calculations 



The optical path difference, </>, measured 

 by any of the preceding methods, can be 

 used to calculate a number of other quanti- 

 ties. The OPD is given by 



<f> = tini — 111) 



a) 



where t is the thickness of the object, W2 its 

 index, and ni the index of the medium 

 through which the reference beam passed, 

 the mounting medium. 



Thickness can be determined directly from 

 equation (1) if the index difference is known. 

 If the object is spherical, cylindrical, or some 

 other regular shape so that its thickness can 

 be determined by lateral measurements, then 

 the index difference can be measured from 

 equation (1). 



If one is free to change and to measure in- 

 dependently the index Ui of the mounting 

 medium without changing that of the speci- 

 men, a second equation can be obtained. 



<A' = t{n2 — ni) 



(^) 



Then both thickness and index, W2 , can be 

 determined simultaneously. 



t = 



rii — nx 



Ui = 



<i>ni — ^'rii 

 4>- 4>' 



(3) 



U) 



Since these equations utilize the differ- 

 ences between measm-ed quantities, care 

 must be taken that the desired precision is 

 not lost. 



A sensitive method for determining the 

 index of a specimen is to change the index 

 of the mounting medium until the object 

 has no interference contrast, i.e., until = 0. 



Of major importance for biological studies 

 is the general rule that the index of a solution 

 of protein in water increases hnearly as the 

 concentration and that the specific refractive 



To image 

 " and eyepiece 



Beam- splitting prism 



Parallel plate 

 compensators 



Object slide 



Parallel plate ■ ' 

 compensators 



Objectives 



Comparison slide 

 Condensers 

 ^-=^^ Step 



compensator 

 * Wedge compensator 

 c 



Beam-splitting prism 

 ntermediate lens 



Fig. 11. The Leitz interference microscope. In 

 this sj'stem the object and reference beams are 

 completely separate and pass through separate 

 condensers and objectives. The horizontal distance 

 between these two complete microscopes is 62 mm. 

 Coarse adjustment of the optical path is provided 

 by the step compensator. This is a rotatable disc 

 on which ten glass plates are arranged so that they 

 can be swung into path of the reference beam. The 

 wedge compensator provides fine adjustment and 

 measurement of the optical path. The motion of 

 the center wedge is measured by a micrometer. 



increment, a, is essentiallj^ the same for all 

 proteins (30). The latter is defined by the 

 equation 



ns — riv 



C 



(6) 



where n^ is the index of the solution, n^, the 

 index of water, n^, = 1.33, and C the concen- 

 tration in grams of dry material per 100 ml 

 of solution. For proteins the average value 

 of a is 0.0018. 



If the specimen of thickness t is mounted 

 in water, the measured OPD is related to 

 the above quantities by 



(6) 



Therefore 



<f> = (ria — nw)t 



<i>/a = Ct. 



(7) 



431 



