where 



the Slit in Interference Experiments. 555 



of th sin 2o> 



p = 7 ; — --rrr, tor trie mirrors, 



(acos2a> + o) 2 ' 



_ (/*-!) (tan a^ + tan « 2 )5 *,,,.. 

 / , 7\2 ior the bipnsm, 



2eFb p l im . 



for the divided lens. 



lah-F(a + b)\* 



Assuming, then, that each element of the slit acts as an 

 independent source of light, the intensity due to the whole 

 slit is proportional to 



/w/2 Pk/2 r 2tt 



I 1 1 + cos — \a + /3x + (ycos# — /3^sin0sin <b)u 



— (y sin + /3'x cos sin (f>)v}~\dudv 



= kl{ 



sin — (7 cos — ft'oc sin sin <£) & sin — (7 sin + j3 f x cos # sin (/>) / 



1+— .— 



— (y cos — /3'x sin sin <f>)k — (7 sin + fi'x cos sin <f>) Z 



A, v ' ' \ 



2tt 

 Xcos-- 



(« + £*)} 



where k is the breadth and I is the length of the slit ; so 

 that the visibility of the interference-fringes is the absolute 

 value of 



sin — (y cos Q—fi'x sin sin <j>) k sin — (7 sin + fi'x cos 6 sin </>) / 



TT , „, . „ . ,v , 7T 



(y cos — £'# sin sin </>) £ — (7 sin + £'# cos sm<p)l 



and thus, unless $ = 0, depends upon the order of the 

 bands. 



When = 0, the visibility is independent of the length of 

 the slit at the point x = 0, and is given by the absolute value 

 of sin (TryJc/\) /(iry 1c/\). On moving away from this point 

 the bands become less and less distinct, disappear when 

 a? = X/($ / sin <£ . I), and then reappear as a set of bands com- 

 plementary to the former, and so on. 



At a given point x of the field the visibility is independent 

 of the length of the slit only if 



tan 0= — —x sin d>= r sin <f>, 



7 T a T 



