454 Prof. Potter on the Principle of Nicol’s Rhomb, 
To find the critical angles for the two rays as they fall upon 
the Canada balsam, we have the law of Snellius if ¢ is the angle 
of emergence, ?’ the angle of incidence within the medium, 
sin #! = ae 3 | 
and when 7 is 90° as its highest value, we have 7 the critical 
angle, which is found from 
we foil 
sinz= —-. 
When the rays pass from one medium to another, « becomes 
the relative refractive index for those media, and in the above 
formula is the quotient of the absolute refractive index for the 
medium in which the ray passes, divided by that for the medium 
into which it emerges; therefore we have for the ordinary ray, 
_ Ho _ 16543 
* ETE Tpse” 
for the extraordinary ray, 
sy He to / 1 —e? cos? 0 
Ke Ke 1 
The former is greater than unity, and 7 in sin?’ sa has a de- 
finite value, which is found to be 
#’ =68° 23). 
The latter, when @ is small, is less than unity, and uM greater 
than unity, and there can be no critical angle; therefore the rays 
will pass into the Canada balsam at. all angles of incidence 
upon it. ee 
Whilst Ke _ Mo V1—e cos? 0 
mae Ke 
will oceur ; and when it equals unity, 2’ will be 90°. To find 
6 when this happens, we have 
remains’ less than unity, this 
Me _ 1 — Ho WV 1—e?co0s?0 
= = 1L > ——_——_» 
Ke Ke 
which gives 0=33° 43). 
Now if 4f, fig. 2, be a natural force of the crystal, the optic 
axis* makes an angle 45° 20! with it; and adding 90°— 33° 43! 
=56° 17! to it, we have 45° 20'+56° 17=101° 37’. If the 
angle ab f were this value, an extraordinary ray falling upon the 
* Huygen’s Traité de la Lumiére, p. 98... 
