Scattering of Light by Small Dielectric Spheres. 419 



av 

 In the limit ,- = — f, we find 

 at 



E __/?^, (3) 



t c 2 r . J 



i /o\ t^ d 2 u, sin 3 



or by (2) E,= - J -j- , 



or by (1) E,= E *=| W "™* sin 2™* ^ wV 



But \« = c, hence 



jb "+ 2 r C 



,-, -n^'— l^o47r 2 sin $ . a 

 E, = E -^ R 3 ~ 2 - — sin 2™*, 



or, if we write e s for E^ the secondary wave can be repre- 

 sented by 



-j-,/'— 1 3 47r 2 sin$ . ( ,v 



^ = E 7 — -K° — -r - - sm 2-7ni(£ — « ), 



where £'= -, ra = - , 



C A. 



™ /c— -1 -r,o 47t' 2 sin $ . 2it , N , JN 



2<7T / 



or g = E s sin — (ct — r) , 



i -n T^^"~ l-no47T 2 sin $ 



where E S = E,— -Pi- —-. s 



k + J X- r 



while the primary wave is represented by 



«=Esin^(rf-«) (5) 



For 3 = 0, the electric and magnetic forces vanish and no 

 light is given out in the direction x of the oscillation of the 



IT 



doublet. For 3 = 9 , the electric and magnetic forces be- 

 come a maximum on the surface of a sphere of radius r. 

 No light is given out in the direction x, which is perpen- 

 dicular to the original plane of polarization ; the light 

 emitted in the vertical plane yz is plane polarized ; it is 

 also polarized in every other direction so that the plane of 

 polarization in every beam is perpendicular to e s (see tig. 1). 

 The energy per unit volume and the intensity of the light 



2 E 2 



