THE RAINBOW DUE TO A CIRCULAR SOURCE OF LIGHT. 



dlj h 



Ix ~ a 



put / =tiin £■ , 



' ax ' 



tlicn £, being the angle between the tangent to the \Yave-front and 

 tlie j-axis or tlie angle between the wave normal and the y-axis, 

 is of the order of ^. It follows that x is of the order ^'. This 

 shows that in (2) d1 was neglected as compared with d. 



Secondly, tlie phase difference at a point x, y, z on the wave- 

 surface is easily calculated from the equation (2), the ;2;-axis be- 

 ing perpendicular to the x and y axes. Represent the position 

 of the observer by ç, vj, o, then the phase difference is 



ö^=V(x-,-)2 + (^/---yf^-r-^/FT^' , 

 or è^o^\d., , 



h - 2^ 



where "i = ^-t-^ — ^' ^2=~ör ' 



X, z, Ç, being small compared with fj. Then the intensity, being 

 proportional to the square of the amplitude, is given by 



where V,= ^— ( a cos^:^f5 ila , V,--= ^— ( a sin ^^u da 



d(T beins: the surface element of the wave surface, and « the 

 amplitude of the wave. In the case of a spherical drop, we 

 have to put 



a = cr sin I , 

 where I is the angle of incidence of the ray which has passed 

 through da, and c depends on I, n, p, representing the effect 

 of polarisation 



or « = cr sin (lo+r) 



where Iq is the angle of incidence of a i-ay of minimum devia- 

 tion and 7- = ! — Iq. But in the position of minimum deviation 



