Intelligence and Miscellaneous Articles. 319 



atmosphere would form, after condensation, a stratum of water the 

 thickness of which would differ but little from 4 centims. — Gomptes 

 Rendus de VAcademie des Sciences, Feb. 12, 1877, tome lxxxiv. pp. 

 285, 286. 



ON THE POLARIZED LIGHT OF THE RAINBOW. 

 BY PROF. J. DECHANT. 



In vol. clix. of Poggendorff's Annalen, M. Schiel communicates 

 the observation that the light of the rainbow is completely polarized. 

 This fact had also previously been observed by Tyndall, in 1870, on 

 the occasion of his journey to Algeria* ; and he also states the 

 direction of the polarization, saying, " The light of the bow could in 

 all cases be extinguished by a Nicol's prism the greater diagonal 

 of which was placed tangential to the arc." 



The phenomenon finds its satisfactory explanation in the reflec- 

 tion of the light at the back of a rain drop. For, in the first place, 

 the direction of undulation of the light which arrives at the eye 

 from the rainbow agrees with that of the polarized light produced 

 by reflection. If, namely, the light of the rainbow is extinguished 

 by the Nicol with its longer diagonal held parallel to the tangent 

 to the bow, the undulations of the light itself take place in the 

 direction of the longer diagonal, consequently parallel to the tangent. 

 But parallel to the tangent is perpendicular to the plane which 

 passes through the sun, the rain drop, and the eye ; hence it follows 

 that the undulations are perpendicular to the plane of incidence. 



Secondly, however, the angle under which the rays fall upon the 

 posterior wall of the drop is not far from the angle of complete 

 polarization ; for while the latter for water in air amounts to about 

 37°, the former averages 40°. 



Calculating according to FresneFs intensity-formula (and taking 

 into account the double refraction in the rain drop) the ratio of the 

 intensities of the light whose undulations are perpendicular to. and 

 of that whose undulations are in, the plane of incidence, we get 

 r cos 3 Q-/3) -p 

 Lcos(a+/3)J ' 

 where a denotes the angle of incidence of the effective rays, and ft 

 the angle of refraction. This gives for the extreme red rays (n= 

 1-3317) 24-5, and for the extreme violet (ws= 1-3448) 34-9. 



Thus the rainbow appears from 25- to 35-fold fainter when the 

 Mcol is rotated 90° from the position in which the shorter diagonal 

 is held parallel to the tangent of the bow — which certainly comes 

 very near complete extinction when we consider that the secondary 

 bow already appears tolerably faint whose intensity according to 

 the calculation is yet only 2^-fold less than that of the primary. 



Lastly, we can also indirectly, by an experiment, convince our- 

 selves of the correctness of the explanation above given, if we try 

 to obtain a rainbow with a liquid in which light is not so strongly 

 polarized by reflection at the back of a drop as in water. [For this 

 purpose we first seek the exponent of refraction of the liquid with 

 which light would be completely polarized. 



* In den Alpen, deutsche Ausgahe, 1872, S. 382. 



