306 



POLARISATION. 



determined by the longer diagonal, while the shorter one is 

 parallel to the principal section. 



The greatest possible inclinations which the incident rays can 

 attain towards the different sides are evidently determined, under 

 the given relations, by the corresponding limiting angle of the 

 total reflexion at the layer of balsam. Let us first trace the 

 direction of the rays deviating in the plane of the paper towards 

 the right. Assuming the refractive index of calc-spar to be 1-6583, 

 and that of Canada balsam (according to Brewster) 

 1'549, then for the ordinary ray the sine of the 



1 .! KOO 



limiting angle = 



precisely what 69 4' 



FIG. 171. 



7 = 



gives for the angle itself. Hence, if kf (Fig. 171) 

 is an incident ray deviating to the right, and f h 

 the ordinarily refracted one, the latter, if it is a 

 limiting ray, forms the above-mentioned angle of 

 69 4' with the normal h g. If we now draw 

 through / a line perpendicular to d c and produce 

 it to g, then 8 is the angle of incidence, 7 the angle 

 of refraction, and z the inclination of the incident 

 limiting ray to the axis. But in the rectangle 

 dfhy we stated above that a =89 IT '; therefore, 

 since the angles at h and / are right angles, 

 g = 90 43'. Whence we obtain 

 180 - (69 4' + 90 43') = 20 13' ; 



sin B = cos e = T6583 sin 7, 



6 = 55 2'. 

 Further, since j3 = e -f ~, that is .* = @ e, we get as maximum 



inclination 100 r Q , 



z = L& DO . 



If again the refractive index of the Canada balsam is assumed 

 to be T528, according to Wollaston, we obtain for the limiting 

 angle of the total reflexion 67 1'. Hence 7 = 22 10', and 

 z =16 44. 



The calculation for the rays inclined towards the other side is 

 not so simple. Here we have the transmitted extraordinary rays, 

 whose limiting angle determines the greatest deviation from the 

 perpendicular ; for the ordinary rays meet the layer of balsam more 

 obliquely the greater the inclination, and therefore always 

 undergo total reflexion. The refractive index of the extraordinary 



and since 



