472 , Scientific Intelligence. 



should lie within the confines of experimental possibility. A 

 similar argument applies in case it should happen that e is 

 negative. — Yerh. d. Deutsch. Phys. Gesell., 9/12, 86, 1919. 



h. s. u. 



8. The General Polarization Surface. — "When light falls upon 

 a plane mirror, — the material of which is single refracting and 

 does not exhibit metallic absorption, — the completeness of 

 polarization will be a maximum when Brewster's condition * = 

 tan -1 n is fulfilled. In general, it is not possible to produce 

 artificially a beam of light having all of its rays strictly parallel, 

 and therefore a wide beam of completely plane polarized light 

 cannot be obtained by reflection at the surface of a plane mirror, 

 even when monochromatic radiation is employed. In partic- 

 ular, the limited cone of rays of circular right section which can 

 enter the eye of an observer, whose line of vision is directed 

 obliquely toward a polarizing plane mirror, will not give a uni- 

 form field of view when the analyzing apparatus is set for 

 extinction. As a matter of fact, under certain conditions of 

 incidence, the field will be crossed by dark bands having the 

 shape of conic sections. The concave sides of the conies will 

 be turned toward the observer. The major axes of the conies 

 will lie in the meridian plane of the reflected solid cone of rays, 

 that is, the plane determined by the axis of the cone (line of 

 sight) and the perpendicular dropped from the center of the 

 pupil upon the plane of the reflector. The arcs nearest to the 

 observer will be elliptical in form while those more remote will 

 be hyperbolic, a single parabola falling between the two sets of 

 loci just mentioned. Since the angular aperture of optical 

 analyzers rarely exceeds 30° or 40°, and as the polarizing angle 

 of glass mirrors is usually from 56° to 60°, the parabolic arc 

 will be outside of the field of view so that hyperbolic arcs only 

 will be observable. 



By suitably curving (by empirical methods) the surface of 

 the mirror Eeuter has constructed cylindrical reflecting polar- 

 izers giving wide uniform fields of view. The curvature of the 

 cylinder will depend, of course, upon the index of refraction 

 and upon the angle of the cone. 



The theoretical form of the surface which will produce the 

 most uniform field, under given conditions, has been investi- 

 gated mathematically by Felix Jentzsch-Grafe. He first 

 derives the partial-differential equation of the surface under the 

 condition that Brewster's law be fulfilled. It is then shown 

 that the general solution of this equation may be written F = g 

 (logr + w</>), where g means any arbitrary function of the argu- 

 ment within the parentheses. It is thus shown that the general 

 polarization surface is generated by the revolution around the 

 proper radius vector of a rigid logarithmic spiral so constituted 

 that the constant angle between any radius vector and the 



