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 88 1° with the plane of refraction for a mode- 

 rate numher of plates, or 88i° 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- 

 mula gives 



Cot ^-=(cos(i-i'))" and ^ = 88° 50'; 

 so that the light should appear to be completely polarized, as it was 

 found to be. 



At an angle of 61° 0' the pencil was polarized by twenty four 

 plates or forty eight surfaces. Here 



Cot ^ = (cos (i -»■'))*« =89° 36'. 



At an angle of 43° 34' the light was polarized by forty seven 

 plates or ninety four surfaces. Here 



Cot d = (cos {i-i'))°' and a =88° 27'. 



It is needless to carry this comparison any further ; but it may be 

 interesting to ascertain by the formula the smallest number of refrac- 

 tions which will produce complete polarization. In this case the an- 

 gle of incidence must be 90°. 



Hence 9 = 56° 29' and (cos (i-i'))^ gives 88° 36', and (cos 

 {i — i')) ' " 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 formulas 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 formulae become 



I cos {i-{-i'y 



Q=Rfl-2_^^ii:i^:iV-) and 

 \ [cos_{i_+i)Y / 



~^\cos (i — i') I 



/ (cos (i-i'))-\ 

 Q' = l -RI 1-2— -) 7^-^ • 



\ (}j+(cos {i -i')y I 



Vol. XXIIL— No. 2. 30 



