66 



PROGRESS IN MICROSCOPY 



be applied later. Let us now investigate the area wherein the small 

 bacterium A lies. Let n be the refraction index of the latter and //' 

 the index of the liquid it is immersed in (Fig. 2.2). Tf the index is 

 slightly larger than /;', the light passing through the bacterium (ray 1) 

 lags in relation to the light traversing the liquid close to the bacterium 



Fig. 2.2. Optical path difference produced by the object A. 



(ray 2). If e is the bacterium thickness, the difference in the optical 

 path is zl = {n — n')e. The sinusoids V^ and K, denote the luminous 

 vibrations propagating along rays 1 and 2, respectively. Since /; > //' 

 Ki lags in relation to V.^. Such lag is denoted by the short distance I 

 in Fig. 2.2. in the following, it is assumed thai the lag is small in 



Fig. 2.3. Graphical rehitions among the F,, V.^ and F, waves such that F, ^--^ K. I F,. 



relation to wave-length I. Figure 2.3 shows both sinusoids Vy and K., 

 side by side and only out of phase by the short distance I, as shown 

 in Fig. 2.2. It is well known that a sinusoid, i.e. Vy or \'.^, can be 

 shown by the equation: y = asmlnxfl, where y is the ordinate 

 of the curve corresponding to abscissa .y, a the amplitude (highest 



