MEASURING REFRACTION INDICES— UNPOLARIZED MICROSCOPES 175 



the object is ne. A random ray (2), passing next to it, follows the 

 path n'e. 



Over and under the horizontal hnes BC and B'C\ respectively, 

 optical paths are identical for the rays (1) and (2) and do not intervene. 

 The path difference between (1) and (2) is then: 



d = (n'-n)e. (6.1) 



This is the path difference brought about by the object. 



The following may apply to any 2-wave interference microscope 

 but, in order to simplify matters, the matter is set forth on the basis 

 of Dyson's interference microscope (Fig. 3.4). Let us consider the 

 rays, paralleling the ray MAC, corresponding to a wave surface which, 

 after passing through the object, has the shape shown in Fig. 6.2. 



1 



Ji 



B C 

 Fig. 6.2. The wave surface after passing through the object. 



The rays paralleling the ray BN, which have not passed through the 

 object, exhibit a flat surface wave. These two waves meet at A' where 

 they interfere: their path difference J depends on the microscope 

 adjustment (Fig. 6.3). In fact, the plates Li and Lo are not parallel- 

 sided plates but small-angled prisms. Hence, the path difference varies 

 continuously from one end to the other of the field of view. If the 

 variation attains several wave-lengths, straight and parallel fringes are 



Fig. 6.3. The two wave surfaces in the image A'. 



developed, as shown in Fig. 6.4. The distance of both waves, i.e. their 

 path difference J, varies: every time J increases or decreases by A, 

 a shift is made from one fringe to another. Assuming that there are 

 three fringes, the field aspect is shown in Fig. 6.5. The object lies 

 in the area A'. It is assumed that, in the area (2) (Figs. 6.4 and 6.5), the 

 path difference J between the two waves is an odd number of times A/2, 

 e.g. 5A/2. Therefore, there is a dark fringe in area (2). If J = 7/1/2 in (1) 



