448 Mr. L. N. Gr. Filon on certain Diffraction Fringes 



but tlie conditions of reflexion, which should be the same for 

 all four mirrors, are altered, and this changes the intensities 

 of the two streams. We shall see afterwards that this silver- 

 ing can be done without impeding the passage of the trans- 

 mitted stream, as it will turn out thnt the two streams must 

 be kept separate. 



p 



Fig. 4. 

 __n\q_. — W 





mC 



A %l — 'Vm¥\ 



!__— — - — — ~~" 



\ 





c i^ 



Suppose then that a plane wave of light whose front is 

 M M / is incident upon the diaphragm. Let us break the wave 

 up, as is usual, in the plane of the diaphragm. Let Z be a 

 point on the screen whose cordinates are (p, q) at which the 

 intensity of light is required. 



Then if C be the centre of the object-glass, the direction in 

 which rays T U, T' U' must proceed in order to converge to 

 Z after refraction is parallel to C Z. 



Hence PQ, RS, TU, P'Q', R'S', T'U' are ail parallel to OZ, 

 and the direction-cosines of CZ are 



*V + ? 2 + 6 2 ' s/'pi + q^ + tf' ^zfi + tf + o* 



I shall assume that the strips e and d are cut from the same 

 plate and are of equal thickness. This will sensibly simplify 

 the analysis, though, as I think, it would not materially influ- 

 ence the appearances if the strips were unequal. 



If, however, we suppose them equal, we may neglect the 

 presence of strips, as far as refraction is concerned, since 

 clearly the retardation introduced is the same for all parallel 

 rays. 



If now UU f be a plane perpendicular to CZ, then, since we 

 know that rays parallel to TU, T'U' converge to a focus at Z, 

 the only parts of the paths of the rays which can introduce a 



