PHYSICAL ASPECTS OF IMAGE FORMATION 3 



such as M, emits luminous vibrations, not only towards the geometrical 

 light-ray MAq but in other directions as well. The various points of 

 the wave surface ^, diffract the light which overspreads on the image 

 surrounding the point A'q. 



Figure 1.2 shows that, A'^ being the centre of the sphere Z., all 

 the vibrations, originated from this wave surface, reach A^^ in the same 

 vibratory state. In order not to over-elaborate the figure, only the 

 vibrations emitted by two points, Mq and Mi are shown. The luminous 

 ampHtude, at A'^ is merely the sum of amphtudes of all vibrations 

 reaching such point. Since intensity of light is proportional to the 

 squared amplitude, squaring of the aforesaid sum determines intensity 

 at A'q. Hence, hght is maximum at A'^. 



Let us now consider the diffracted vibrations reaching the random 

 point A[ of the plane .t (Fig. 1.3). Since point A[ is removed from 

 the sphere's centre, the distances from the various points of 27,- to A[ are 

 no longer equal. Hence, the vibrations emitted by i7. do not reach 

 A[ in the same condition. In the case of Fig. 1.3, both points M^ 

 and M emit vibrations which are in opposition at A[. If ?. is the 

 wave-length, then: A[M—A[Mq = /.jl: both vibrations are cancelled 

 out: the luminous amphtude at A[, originated by M^ and M is 

 zero. 



It follows that intensity at ^^ is the outcome of all points 

 of the wave surface i7,. and not merely that of points Mq and M 

 only. 



Computing the phenomenon discloses the following: the image of 

 the luminous point A is shown by a very bright, circular, central disk 

 (Fig. 1.4), surrounded by alternately bright and black rings whose 

 intensity decreases rapidly as distance increases. Only two or three 

 luminous rings are usually visible in a microscope as the others are 

 absorbed by the stray light and, therefore, too weak. The curve in 

 Fig. 1.5 shows the distribution of light-intensity in the diffraction 

 pattern. Ordinates show the intensities; abscissae are determined by 

 the parameter Z which depends not only on the geometrical distance 

 from the centre A'^ but also on the characteristics of the microscope's 

 objective. If g is the objective magnification and C the geometrical 

 distance from the point Aq to the point where the light intensity is to 

 be calculated, the diffraction theory conduces to write: 



_ 27777 sin w C 



Z = ~ (1.1) 



^ g 



