McClellan — Note on Interference with the Bi-Prism. 295 



from I 2 will illuminate S 2 T 2 . The space S X S 2 is lit by both 

 sources and is therefore the interference field. It is necessary to 

 notice however that as no light from l x can fall below S„ the prism 

 face OP 2 can be looked upon as an opaque screen for I r Con- 

 sequently we find diffraction bands extending from S x into SjS a . 

 In like manner fringes will extend inwards from S 2 . ]STow it 

 is easily seen that if the two sets of diffraction fringes should 

 extend so far into SjS, as to meet, there would be no clear field 

 in which pure interference could be seen. The two kinds of 

 bands would be superimposed, and neither would be seen as they 

 are. This, of course, is precisely what does happen if condi- 

 tions are not arranged to prevent it. It is easy to find what 

 these conditions are. 



Let the distance from light to prism be &, and that from prism 

 to screen be o. Let the angle OPjP,, be e. Then if d be the 

 angle I 1? OL and u the index of refraction, d = (u — l)e which 

 is half the angular space S x OS 2 . The half interference field on 

 the screen is then b(u — l)e. 



Now regarding OP 2 as a screen for the source I 15 and x as 

 the distance of the 2wth diffraction band from the geometri- 

 cal shadow, 



* = /*< 



— - 2nX 



it is evident that if we are to have an open field for pure inter- 

 ference, this distance x must be less than the half interference 

 field, that is, 



/ 



b(a + b) 



— '- 2n\ < o{u — l) e 



or reducing 



1 1 (u-l)V 

 a b ^ 2??X 



for any given prism, u and e can be measured, n is a constant 

 for all prisms, and is simply the number of that pair of bands 

 for which the ratio of intensities is so close to unity as not to 

 permit of separation by the eye. This value can be calculated 

 or observed. Either method shows that six is a fair value for n. 

 \, of course, depends upon the light used. It should be noticed 

 that while a prism with a large angle e, according to the for- 

 mula, will give a clear space more easily, the interference lines 

 will be narrower the larger the angle. This is shown by the 



expression for the width of interference lines, — — . For 



this reason the prisms supplied for this purpose usually have 



