456 Prof. Potter on the Principle of Nicol’s Rhomb. 
and the angles of the prisms as investigated below. In fig. 3, 
let acbd be the plate of air between a prism of cale-spar ac bdefg, 
and a like prism of glass acbdhk, Now if fig. 4 represents a 
Fig. 3. Fig. 4. 
principal section of the rhomb, ab being the section of the plate 
of air, a ray of light Sr being incident nearly perpendicularly at 
r on the surface J f will furnish an ordinary ray 70 and an extra- 
ordinary ray re with the angle evo between them nearly 6° 40. 
Then if the ordinary ray falls at the critical angle 37° 12! and 
any higher angles, it will be totally reflected and thrown aside as 
om in the figure. The critical angle for the extraordinary ray 
will depend upon the inclination of 4a to the optic axis. If we 
take bf a natural face of crystal, and the angle ab f equal to 40°, 
we find the critical angle ¢” from the expression 
a eee 
Re by V1 —e? cos? 0 
where 6 is measured from the major axis of the generating ellipse 
of the oblate spheroid, the angle the minor axis makes with bf 
being 45° 20’. 
In fig. 5, let ad and Of be asin Fig. 5. 
fig. 4, let bu be perpendicular to 
ab; let 6A be the direction of the 
optic axis and minor axis of the 
ellipse, 6 B that of the major axis, 
and Jr the direction of the extra- 
ordinary ray; then the angle 
A ba=45° 20'—40°=5° 20! 
=angle Bbn; and anglerbn=1", 
therefore 0 =angle rb B=i"+5° 20!, and 
‘60449 
/1—:19605 cos? (i+ 5° 20)’ 
which gives i! about 39° 323!. 
sin 7! = 
