Crystalline Reflexion and Refraction. 



66 



the plane of incidence an angle ^'3 determined by the second of fonnulae (39). 

 By putting t2= t, in that formula, and employing the expression (44), we first 

 obtain 



cos(f, + t'Jcos0'tanw'+sin'(t,4-t'J _ cos(t,4-t',)tan(;? — t'3)+sin(t, + t'J_ 



tane'. 



and thence 



sin 0' tan w' 



sin & tan w' 



tan0'„ = 



sin (p + 4,) _ sin {p + 1,) cos la 



/ 



^ti /^ t_ ^ ^A' 



sin0'tanw'cos(p— 1'2) sin (^ cos (p— 4) ' 



and finally, 



tan0'3:=sin(j)-J-t,)cotan5'; (71) 



a result which shows that the plane of polarisation of the reflected ray is perpen 

 dicular to a plane drawn through the ray itself and the axis of the crystal. U/kvli c a 



Moreover, we find, from the first of formulae (39), by proceeding as above, /^ // r: 



tanf^'i^ — sih(j>T-(,)cotan5'= — cotan0; (72) 



and from (38) it is evident that^,= 0. Therefore all that relates to the case 

 under our consideration may be summed up in the following statement : 



When N = B, and the incident light is polarised in a plane passing through 

 the axis, the course of the light is unaltered, and there is neither reflexion nor 

 refraction. When it is polarised in the perpendicular plane, all the light which ' 



enters the crystal undergoes extraordinary refraction. Whatever light is reflected, 

 is always polarised in a plane at right angles to that which passes through the 

 reflected ray and the axis of the crystal ; and this is true, whether the incident 

 light is polarised or not. 



Here, for the present, we must terminate our deductions from the general 

 theory propounded in this paper. Several other questions remain to be discussed, 

 such as the reflexion of common light* at the first surface, and the internalf 



* The mode of treating the case in which common hght is incident, has been pointed out at the 

 bottom of p. 40, 



"f I have since found that the problem of reflexion at the second surface may be reduced to that 



' of reflexion at the first surface, by means of a very simple rule. Let us suppose the two surfaces of 



the crystal to be parallel; and let a ray r,, uniradially polarised, and incident on the first surface, 



give the ray R^ by reflexion, and the single ray R, by refraction. Let B, be the ray which suffers 



internal reflexion at the second surface, thereby giving the two reflected rays E,,, r',;, and the single 



/u 



7^ 



4^ 

 /A. 



/} VOL. XVIII. J J i ) / ' / '^ -9 



