Crystalline Reflexion and Refraction. 



61 



^ 



thl /dt/ /if f 

 y is / 



We have seen that the deviation always vanishes when the axis of the crystal 

 lies in the plane of incidence. The reason is, because the crystal is then symme- 

 trical on opposite sides of that plane. In this case the problem of reflexion offers 

 peculiar facilities for solution, since the uniradial dii'ections are obviously parallel 

 and perpendicular to the plane of incidence. Let us therefore consider the case 

 at length. 



1. In the first place, when the only refracted ray is the ordinary one, 

 t hree t ransversals are in the plane of incidence, and the transversal of each ray 

 proportional to the sine of the angle between the other two rays. Hence the 

 proportions are 



the same as in ordinary media. 



2. In the second place, when the sole refracted ray is the extraordinary one, / yT^ 

 the three transversals are perpendicular to the plane of incidence ; and, if we use / 

 accents to mark the quantities connected with this ray, we have the equations 



/^. 





which give the proportions 



T\ 



/, 



Ts 



wherein 



-V- 



TOi+Tw'j )lmi nil — in': 



ni^ _ sin 2i^ ± 2 sin^t'^tan e' 

 m, ~ sin2(, ' 



(61) 



(62) 

 (63) 



' ^ 4ci^ £, 



by (26); the upper or lower sign being taken, in the numerator of (63), accord- 

 ing as the refracted ray or its wave normal makes the smaller angle with a 

 perpendicular to the face of the crystal. 



To find the polarising angle, we have only to make m{=m\, for then t'j will 

 vanish by (62) ; and therefore, if common light be incident, the whole reflected 

 pencil will be polarised in the plane of incidence. Supposing the crystal to be 

 a negative one, let us conceive the refracted ray to lie within the acute angle 

 made by the axis of the crystal with a perpendicular to its surface. We shall 

 then have to take the positive sign in the numerator of (63), and the polarising 

 angle will be given by the condition x? />v 



f // ^ 



PrA. 



