PHENOMENA OF PHASE MICROSCOPES 31 



are worth summarizing as the following important and practical theorem 

 (Theorems): 



// the optical path of the particle exceeds the optical path of its surround 

 by a small amount, the particle will appear bright or dark according as the 

 optical path of the conjugate area of the diffraction plate is increased or 

 decreased by 3^ wavelength with respect to the optical path of the comple- 

 mentary area. If, on the other hand, the optical path of the surround, 

 exceeds the optical path of the particle by a small ainount, the particle will 

 appear bright or dark according as the optical path of the conjugate area is 

 decreased or increased by }/i wavelength with respect to the optical path of 

 the complementary area. Furthermore, the contrast in the image is near 

 optimum when enough absorbing material is added to the conjugate area to 

 equalize the amplitudes of the undeviated and deviated waves which arise by 

 diffraction at the object specimen. 



The practical importance of this theorem is enhanced by the fact that 

 also its converse is true (Theorem 4): 



// the particle appears bright or dark according as the optical path of the 

 conjugate area is increased or decreased by ^ wavelength with respect to 

 the complementary area, then the optical path of the particle exceeds the 

 optical path of an equal thickness of its surround. If, on the other hand, 

 the particle appears bright or dark according as the optical path of the 

 conjugate area is decreased or increased by }/^ wavelength with respect to the 

 optical path of the complementary area, the optical path of the particle is 

 less than the optical path of an equal thickness of the surround. The 

 conjugate area of the diffraction plate coincides with the image of the 

 opening in the diaphragm of the substage condenser. This image is 

 projected by the substage condenser and the intervening lenses of the 

 objective upon the diffraction plate and is clearly visible as the brightly 

 illuminated area when the objective is viewed down through the body 

 tube in the absence of the eyepiece. Whether or not the quarter-wave 

 coating has been applied to the conjugate area or to the adjacent comple- 

 mentary area can be ascertained from the catalogue data of the phase 

 objective. From this important information it is possible to determine 

 from the above theorem whether the refractive index of the particle is 

 higher or lower than the refractive index of its surround, provided that 

 the optical paths of the particle and the surround differ only slightly, 

 for example by %o wavelength or less. 



We have seen that, as the optical path difference A between the 

 particle and the surround approaches zero, the amplitude of the deviated 

 wave approaches zero also. This means that in order to obtain optimum 

 contrast it is necessary to add increasing amounts of absorption to the 



