258 Lord Rayleigh on the Remarkable Phenomenon 



the band begins to widen *, in consequence of the less precise 

 adjustment of wave-lengths now necessary. At higher 

 angles the reflexion may be sensibly total over a band of 

 considerable width. All this agrees precisely with Prof. 

 Stokes's description of the case considered by him to be typical. 

 The movement of the band towards the blue end of the 

 spectrum is to be attributed to the increasing obliquity within 

 the crystal, as in the ordinary theory of thin plates. 



It thus appears that if we allow ourselves to invent a suitable 

 crystalline structure, there need be no difficulty in explaining 

 the vigour and purity of the reflexion ; but such an exercise 

 of ingenuitv is of little avail unless we can at the same time 

 render an account of the equally remarkable circumstances 

 stated in (1) and (4). When the incidence is in the plane of 

 symmetry, no reflexion takes place. As Prof. Stokes remarks, 

 this might be expected as regards light polarized in the plane 

 of symmetry ; but that there should be no reflexion of the 

 other polarized component is curious, to say the least. Not 

 less remarkable is it that when the incidence is in the perpen- 

 dicular plane, the reflected light should show no signs of 

 polarization. The phenomenon being certaiuly connected 

 with the doubly refracting property, we should naturally have 

 expected the contrary. 



The investigation of the reflexion from a twin-plane, con- 

 tained in the preceding paper (pp. 246 et seqq.), shows, however, 

 that the actually observed results are in conformity with theory. 

 In the plane of symmetry there should be no reflexion of 

 either polarized component, at least to the same degree of 

 approximation as is attained in Fresnel's well-known formulae 

 for isotropic reflexion. As regards light reflected in the 

 perpendicular plane, theory indicates that if the incident light 

 be unpolarized, so also will be the reflected light. Again, 

 the intensity of the (unanalyzed) reflected light should be 

 independent of the polarization of the incident. So far there 

 is complete agreement with the observations of Prof. Stokes. 

 But there is a further peculiarity to be noticed. Theory 

 shows that in the act of reflexion at a twin plane, the polariza- 

 tion is reversed. If the incident light be polarized in the 



* It should be observed that if the spectrum be a prismatic one, there 

 is a cause of -widening which must be regarded as purely instrumental. 

 According- to Cauchy's law (/i=A+BX— 2), 



o>=-2BX-3SX; 

 so that if the band correspond in every position to a given relative range 

 of X ; its appaient width (reckoned as proportional to S/x) will vary asX -2 . 

 In a diffraction-spectrum this cause of widening with diminishing X 

 would be non-existent. 



