INTERFERENCE OF LIGHT. 89 



These results are in exact accordance with theory. 

 In fact, since On = nk, and V = n'k, the difference of the 

 paths traversed by the reflected rays, 'knm and kn'm, when 

 they meet at m, is the same as if they had reached that point 

 diverging directly from the points and O x . All, then, that 

 has been said respecting the interference of the pencils di- 

 verging from two near luminous origins, will apply to this 

 case. Since &Q = OQ = O'Q, the line QP, which bisects the 

 line 00', is also perpendicular to it, and any point of it, as 

 A, is equidistant from and 0'. The bands, therefore, are 

 symmetrically situated with respect to this line ; and the dis- 

 tance, Aw?, of the band of any order from the central band is 



wAAP 



equal to -QQT-. 



This distance is easily expressed in terms of given quan- 

 tities. For PQ = OQ x cos OQP = A-Q x cos OQP ; and 

 00' = 20P = 2&Q x sin OQP. But since the angles QO, 

 &Q0 7 , are bisected by the lines Qw and Q, x , it is easy to see 

 that the angle OQP (or the half of the angle OQO') is equal 

 to the inclination of the mirrors. If then this inclination be 

 denoted by , and the distances &Q and QA by a and b, we 

 have 



00' = 2a sin e, AP = a cos + b <= a + b ; q. p. ; 



and therefore the distance of the band of the n th order from 

 the centre is expressed by the formula 



(a + b) n\ 

 2a sin c 



The measurement of the distances is most conveniently 

 made by means of a lens, having in its focus a finely divided 

 scale cut with the diamond upon a piece of parallel glass. 

 The fringes so measured are those formed in the focal plane 

 of the lens. 



