Phenomena of Reflection of Light. 417 



the refractive index, and the imaginary portion is proportional 

 to the product of the refractive index and the coefficient of 

 absorption. If we chose as unity the velocity in pure ether, 

 the real part is the Refractive Index, n, and the imaginary 

 portion is nh. 



In total reflection, C 2 , as we have seen, is a pure imaginary, 

 i. e., no waves are propagated in the second medium perpen- 

 dicular to the surface. In the general case of light meeting 

 the surface separating two media, waves are propagated in the 

 second medium with some absorption, i. e., C 2 is complex. Fig. 

 5 represents a typical case of so-called Metallic Reflection. 

 We will suppose that the first medium has no appreciable 



absorption. As in previous figures, 13 = — , 16 = A 2 , 63 = C^, 

 65 = C 2 2 , 15 = — a . C„ 2 , (65), being complex, the mean propor- 



tional between it and 63 will be 62, whose length is the arith- 

 metical mean proportional and such that the angle 263 is half 

 the angle 563. 



Since — - = — , the phase difference must decrease from ir at 

 R s 12 



perpendicular incidence (6 at 1), to zero at grazing incidence 



32 



(6 at 3), while the phase of R, = - - J - varies from zero to it. At 

 1 34 



the Principal Incidence, I, the phase difference is — or 14 and 



14 

 12 are at right angles. The numerical value of — is the 



Principal Azimuth. 



To determine the refractive index, n, and the coefficient of 



absorption, k, we extract the square root of — ,, (15). The 



real part of the root is n ( — being unity J and the imaginary 



portion is nk. 



Fig. 5 represents reflection from copper in air, when the angle 

 of incidence is 71° 35', the Principal Incidence (Drude). The 



velocity of light in air, v 1} is taken as unity and — - 2 is repre- 

 sented by 13. 16 = A 2 = sin 2 71° 35', and 63 = C x 2 = cos 2 

 71° 35'. The Principal Azimuth of copper is 38° 57'. Since 



at the principal Incidence, I, the difference of phase is — , 12 



