672 Prof. Nihal Karan Sethi on the Diffraction 



It will be seen from what follows that these features are in 

 agreement with the observed changes in the visibility of the 

 interference fringes in different directions. 



4. Theory. 



The effects observed may be explained on elementary 

 principles in the following way : — 



Let AQC (fig. 1) represent the principal section of the 

 cvlinder, and let XA and YPQ be parallel rays falling on it. 

 The ray XA will follow the path ABCD, and the ray YPQ 



Fig-.l. 



incident at an angle greater than the critical angle will be 

 totally reflected along QRS parallel to CD, if the angle of 



incidence at Q is equal to -~ — (r — i), where i and r are the 



angles of incidence and refraction at A. These parallel 

 rays CD and QRS most interfere when they are brought 

 to a focus by a lens (e. g. of the eye*). The difference of 

 path between the two rays is evidently 



S = 2[PQ-^.AB] 



= 2a\_cosi 

 = 2a (sin i- 



sin (r — i) — yu-cos r] 

 N cos i~\ 



")L 00Br — ; jr]> 



where a is the radius of the cylinder and fx its refractive 

 index with respect to the liquid. This vanishes at the 

 critical angle when sini = ^. In Table I. are set forth the 

 values of 8 for various angles of incidence i, in a case where 

 ^ = •99 and the diameter of the cylinder was *5 cm., which 

 may be taken to be 10 4 X. The angles of deviation 

 A = 2(r — i) are also shown. 



* There will also be a third ray diffracted from the edge of the 

 cylinder, but its effect is riot appreciable except at small obliquities, and 

 then it practically coincides ^vith QRS. 



