16 AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



ference of the two waves, depends on the amphtudes a^ and a.g of the two 

 waves and on the phase difference d/\ between the two waves. Suppose 

 that the P and aS waves have the same amphtiide and zero phase differ- 

 ence. They then coincide as in Fig. II. 2.4. The amphtude of the 

 resultant wave (P + *S) is twice as great as the amphtude of the P or S 

 wave. Evidently the two waves add or interfere with maximum effect 

 when their phase difference is zero. Waves are said, accordingly, to 

 interfere constructively when their phase difference is zero. Suppose, 

 on the other hand, that the P and S waves have the same amplitude buit 

 differ in phase by ^2 wavelength. A crest of one wave is then displaced 

 over a trough of the second wave, as in Fig. 11.25. The amplitude of 

 the resultant wave (P + S) is zero, and so the two waves destroy one 

 another. Evidently the two waves add or interfere with minimum efTect 

 when their phase difference is 3^ wavelength. Waves are said to inter- 

 fere destructively when their phase difference is ^4, wavelength. 



As we shall see, constructive and destructive interference of light 

 waves of equal amplitude form the physical means for obtaining brightest 

 or darkest contrast in the image of the object particle in phase micros- 

 copy. 



The brightness of an area that is illuminated by a light wave is 

 proportional to the square of the amplitude of the wave. If the area is 

 illuminated by two waves that belong to the same wave train emitted 

 by an elementary particle in the source of light, the brightness of the 

 area is proportional to the square of the amplitude of the resultant wave 

 formed by the interference of the two waves. 



3. A QUALITATIVE EXPLANATION OF PHASE MICROSCOPY 



We shall suppose that the object specimen consists of a single particle 

 which is surrounded by a homogeneous medium. The primary'' purpose 

 of the microscope illuminator and substage condenser is to illuminate 

 the object specimen in a controlled manner. If the source of light is 

 focused upon the iris diaphragm of the substage condenser, as it is when 

 the system has been adjusted for Kohler illumination, the opening in the 

 condenser diaphragm may be regarded as the source of illumination. 

 Light waves radiate from each point in the condenser diaphragm. 

 These light waves are incident upon the object specimen, are diffracted 

 by the specimen, and are subsequently refocused by the objective to 

 form the complete image of the specimen. In discussing the properties 

 of the complete image, we shall avoid a great amount of difficulty by 

 considering only the image formed by a light wave that is radiated from 

 a single point in the condenser diaphragm. We may suppose that, ex- 

 cept for certain refinements which fall outside the scope of a rudimentary 



