[ 366 ] 



XLI. On Extraordinary Reflection. By Arthur Hill Curtis, 

 LL.D., Professor of Natural Philosophy in the Queen's Uni- 

 versity*. 



IN no elementary treatise on Experimental Physics with which 

 I am acquainted is any reference made to extraordinary Re- 

 flection ; and I have known several instances where, from this 

 omission, students have been led, though somewhat illogically, 

 to the inference that in crystals producing double Refraction 

 the ordinary law of Reflection is satisfied. On the other hand, 

 in memoirs on molecular mechanics attention has frequently 

 been drawn to the fact that the construction of Huyghens is as 

 applicable to reflection as to refraction. Professor Haughton 

 draws attention to this fact in his memoir on the equilibrium 

 and motion of solid and fluid bodies (Trans, of the Royal Irish 

 Academy, vol. xxi. part 2) . Mr. Stoney has applied Huyghens's 

 construction to the doubly reflected rays producing rings in 

 striated calc-spar (Trans. R. I. A. vol. xxiv.) ; and Professor 

 MacCullagh has, in the case of light, by the aid of his theorem 

 of the polar plane, determined, on his theory, the intensities of 

 the two reflected rays (Trans. R. I. A. vol. xviii. part 1). Still, in 

 an experimental point of view, the existence of double reflection 

 seems to be generally overlooked. If we suppose a wave-plane 

 to traverse a crystal surrounded by any medium, whether ordi- 

 nary or extraordinary, when this wave-plane reaches the extreme 

 surface of the crystal it will give rise to two inflected rays, and 

 to one or two refracted rays according as the surrounding medium 

 is ordinary or extraordinary. To take the case most easily sub- 

 jected to experiment, let us suppose a crystal surrounded by air, 

 and a ray of light to fall upon it ; part of this light is reflected, 

 and part is refracted, the latter portion being in general divided 

 into two rays, whether the crystal be uniaxial or biaxial ; each 

 of these rays will suffer double reflection at the point where it 

 reaches the bounding surface of the crystal; and in the case 

 where the two surfaces of contact of the crystal with the sur- 

 rounding medium are parallel planes, or, more generally, when 

 they intersect in a line parallel to the incident wave-plane, it is 

 easy to see that theplanes of polarization of thepair of reflected rays 

 corresponding to any one of the two refracted rays produced at 

 the first incidence, are the same as those corresponding to the 

 other ; for it is obvious that, when the above condition is fulfilled, 

 the rays and wave-normals of one pair are parallel to those of the 

 other ; and whatever theory of light be adopted, the plane of 

 polarization is known when the plane of the ray and wave- 

 normal is determined. This is not only true of the two pairs of 

 reflected rays while within the crystal, but, for the same reason, 



* Communicated bv the Author. 



