~ 
On Polarization of Light by Refraction. 233 
eight plates, or sixteen surfaces of parallel plate glass at an angle of 
78° 52’. Now I have ascertained that a pencil of light of this in- 
tensity, will disappear from the extraordinary image, or appear to be 
completely polarized, provided its planes of polarization do not form 
an angle of less than 882° with the plane of refraction for a mode- 
rate number of plates, or 884° for a considerable number of plates, 
the difference arising from the great diminution of the light in pass- 
ing through the substance of the glass. In the present case the for- 
wala gives 
Cot é=(cos(t—7’))'* and 6=88° 50’; 
so that the light should appear to be completely olesheed, as it was 
found to be 
 Atan Gale of 61° 0’ the pencil was polarized by twenty four 
plates or forty eight surfaces. Here 
: Cot = (cos (i—i/))*® =89° 36’. 
At an angle of 43° 34’ the light was polarized by iar seven 
plates or ninety four surfaces. Here 
*Cot é=(cos (i —2’))°* and 6=88° 27’. ; 
It is needless to carry this comparison any furtber ;. but it. may be 
interesting to ascertain by the formula the smallest number of refrac- 
_tions which will produce complete polarization. An this case pate 
gle of incidence must be 90°. iene gt 
Hence 9=56° 29’ and (cos (i—7’))° gives 8° 36/, and ons 
(i—7’))'° 89° 4’; that is, the polarization will be nearly complete by 
the most oblique transmission through four and half plates or nine 
surfaces, and will be perfectly complete through five plates or ten 
surfaces. 
_ Having thus obtained formule for the quantity of light polarized 
by refraction and reflexion, it becomes a point of great importance 
to compare the results which they furnish. Calling R the reflected 
light, these formula become 
(= —, 
cos (7 — 2’) ) a 
(t+i 4 
cos (i—7’) 
war BG Gy) 
Vou. XXIII.—No. 2. 30 
Q=R{1-2 
