418 Ewell — Phenomena of Reflection of Light. 



and 14 are drawn at right angles, in the ratio 14 : 12 = tan 

 38° 57', and such that 24 is bisected at 6. From the pre- 

 ceding, go = dCg and 64 == — C^C,. C„ 2 = 65 is now con- 

 structed. Since 62 is a mean proportional between 63 and 65, 

 the angle 563 is made twice angle 263 and the length of 65 is 



such that 62 2 = 63 X . 65. — = A 2 + C 2 2 is then 15. The point 5 



being determined, the relative amplitudes — and phases 



(angle 412) may be determined for any angle of incidence, *, 

 since sin 2 i = 16 and 62 = — 64 is a geometric mean proportional 

 between 63 and 65. 



Let is be the geometric square root of 15 (or the numerical 

 square root at an angle 816 = \ angle 516). The real part, 

 19, is the refractive index, n, and the imaginary part, 98, is nk, 

 where k is the coefficient of absorption. Fig. 5. gives, for 

 copper, n = "62, nk = 2 - 6, hence k = 4'1. 



It is not difficult to show also that k is the tangent of twice 

 angle 124, which is half the angle 263 (Drucle's Q). 



R s / = — j-j is numerically # 94 and the angular difference of 



phase (angle 234) is 167°. 



The intensity of the reflected light is : 



-m 





(which equals 1'46 for the above illustration, the incident 

 intensity being 2 or 73 per cent), and evidently increases rapidly 



w T ith increase of the imaginary portion of — , -i. e., of k, thus 



illustrating Selective Reflection. 



Worcester Polytechnic Institute, 



Worcester, Mass., August, 1907. 



