150 ON A NEW CASE OF INTEKFEEENCE 



While examining this important experiment the adjustment 

 of which is a matter of some delicacy it occurred to me that the 

 fact of direct interference might be shown in a yet simpler man- 

 ner, by the mutual action of direct and reflected light. An inter- 

 ference of this kind was assumed by Young to account for some 

 of the phenomena of diffraction ; but Fresnel showed that the 

 explanation was incomplete, and that the phenomena in question 

 were caused merely by the interference of the secondary waves, 

 reflexion playing no part in their production. Under these cir- 

 cumstances it is somewhat strange that the fact of the interference 

 of direct and reflected lights should not have been itself submitted to 

 the test of experiment ; especially as the character of this interfer- 

 ence, if it were found to exist, might be expected to throw some 

 light upon the laws of reflexion itself. 



The theory of such interference is easily deduced from the 

 general principles. Let light proceeding from a single luminous 

 origin fall upon a reflecting surface, at an incidence of nearly 90 : 

 a screen placed at the other side of the reflector will be illumi- 

 nated, throughout a certain extent, by both direct and reflected 

 lights ; and, if the difference of the paths traversed by these lights 

 amounts only to a small multiple of the length of an undulation, 

 the two lights will form fringes by their interference. 



Let the intensities of the direct and reflected lights be 

 denoted by 2 and a' 2 , and that of the resulting light by A~ ; 

 then, by the theory of the composition of coexisting vibrations, 

 we have 



A* = a~ + 2 oof cos 2ir 



and V denoting the lengths of the paths traversed by the two 

 waves, from their origin to any given point, and X the length of an 

 undulation. 



The intensity of the resulting light will be a maximum, and 

 equal to (a + a') 2 , at these points for which 



cos 2 TT = + l , or y _ g = 2n 



It will be a minimum, and equal to (a - a') 2 , when 



r 



