68 



PROGRESS IN MICROSCOPY 



provided 7 remains small. Let us now consider the image P' of the 

 specimen P (Fig. 2.4). The bacterium image A[^ is the outcome of the 

 compounded vibrations V.2, and K3, phase shifced by njl and reaching A'^^. 

 Classical rules of vibration compounding show that when two vibrations 



tSS^;::a.;.v. 



^x^^>^. 



Fig. 2.4. In the image A'q, sinusoid (^3 (diffracted light) is shifted by /u/4 in relation to 



the sinusoid V^ (direct light). 



are out of phase by nil (lag of XjA) the squared amplitude of the 

 resulting vibration, i.e. the light-intensity in the bacterium image A'q, 

 is given by summing the squared amplitudes of the constituent vibra- 

 tions V2 and F3. 



Since 9'^ is disregarded, the intensity /^ in the image A'q is given by: 



h- 1 + r^i 



(2.2) 



In random point P' , where there are only direct vibrations whose 

 amplitude equates unity, the intensity is, then, 



Light intensity is the same at all points of the image P': the 

 bacterium is invisible . 



Let us assume that, by means of a suitable experiment described 

 later, it were possible to dephase again the sinusoid Kg by nil. Let us 

 now observe the image P' under such conditions. The vibrations V2 

 and Kg, reaching the imaged bacterium, are shaped either as shown 

 in Fig. 2.5, (a) and (b), respectively. The diffracted vibrations V^ lead 

 in relation to direct vibrations V.^, or, which amounts to the same 

 thing, the direct vibrations V^ are lagging in relation to K3. In the 

 case of Fig. 2.5(b), the converse occurs. Both vibrations, K, and K3, 

 are in phase in Fig. 2.5(a) and, then, the resulting amplitude equates 



