Phenomena of Reflection of Light. 413 



The method, in brief, consists in representing by lines the 

 reciprocals of the velocities of light in the two media between 

 which reflection occurs, and also their components parallel and 

 perpendicular to the surface. These lines are so chosen that 

 very simple geometrical quantities represent Fresnel's Laws, 

 which are assumed, together with the ordinary laws of reflec- 

 tion and refraction. As the lines and angles vary with the 

 angle of incidence and the optical constants of the media, the 

 relative amplitudes, phases, etc., are given by simple geomet- 

 rical relations. 



Light is reflected at the surface, separating medium (1) from 

 medium (2). Let C 1 and C 2 be the components, normal to the 



surface, of the reciprocal velocities, — and — (fig. 1). Let i 



be the angle of incidence, or reflection, and r the angle of refrac- 

 tion. Since the angles of incidence and reflection are equal 

 and since the ratio of the sines of the angles of incidence 



and refraction is v^-r-v^ the components, A, of —and—, parallel 



to the surface, are equal. 



For simplicity, we will take as unity the components of the 

 incident light vibration, parallel and perpendicular to the plane 

 of incidence (i. e., the light is polarized- at 45°). Let the 

 amplitude of the component of the reflected vibration, parallel 

 to the plane of incidence, be R p , and of the perpendicular 

 component, R s . Fresnel's Laws of Reflection are then : 



_ sm(i-r) R p _ cos(i + r) _tan(z— r) 



sm(i + r)' R s ~~ cos («'— r)' p— tsm(i + r) 

 From the above figure and notation, 



sin i = Av x , cos i = C^,, sin r = Av„ cos r — C 2 u 2 

 Substituting : 



__ c-c , R p A'-C. C, 

 s 0, + c; r s - a' + c^c, 



The latter is of course the more interesting and important. 

 The product of the two will give R p . 



C /C, x- c,c, > 



< - - - C - - - -> 



-AW x C(^0 



(1) 



These quantities will be represented graphically. Horizontal 

 distances we will consider real, and positive if to the right. 



