Transparent Plates upon light. 33 



" A pencil of light reflected from the second surfaces of trans- 

 parent plates, and reaching the eye after two refractions and an in- 

 termediate reflexion, contains at all angles of incidence from 0° to 

 the maximum polarizing angle, a portion of light polarized in the 

 plane of reflexion. Above the polarizing angle the part of the pen- 

 cil polarized in the. plane of reflexion diminishes till cos {i-\-i') = 

 (cos {i—-i') ) ^, when it disappears, and the whole pencil has the char- 

 acter of common light. Above this last angle the pencil contains a 

 quantity of light polarized perpendicularly to the plane of reflexion, 

 which increases to a maximum and then diminishes to zero at 90°. 



Let us now examine the state of the pencil C S' that has suffered 



only one refraction and one reflexion. Resuming the formula 



cos {i-\-i') . . . 



tan (p'==7 y- — =7VTT, it is evident that when (cos (i — i'))^=^cos 



^ (cos (t— i'} )^' V v yy 



(i+iO' 9'=45°, and consequently the light is restored to common 

 light. This takes place in glass at an angle of 82° 44'. At all an- 

 gles beneath this the pencil contains light polarized in the plane of 

 reflexion ; but at all angles above it, the pencil contains light polari- 

 zed perpendicular to the plane of reflexion, the quantity increasing 

 from 82° 44'. to its maximum, and returning to its minimum at 90°. 

 By comparing these deductions with the formula and table for 

 reflected light given in my paper On the Laws of the Polarization 

 of Light by Refraction, the following approximate law will be ob- 

 served. When 



Cos {i — i') =cos {i+i') All the incident light is reflected. 

 (Cos (i— *0) ^ =cos {i-{-i') Half the incident light is reflected. 

 (Cos (i — i'))^=cos {i-\-i') A third of the incident light is reflected. 

 (Cos(i- i'))"=cos (i-h*0 An nth part of the incident light nearly 



is reflected. 

 This law deviates from the truth by a regular progression as n 

 increases and always gives the value of the reflected light in de- 

 fect. Thus 



Angles of Incidence. Values of'n. Differences. 



..... 2 .... . 



3 ..... 12 



4 ..... 21 



...... 8 38 



. . . . . 11 . . . = = 43 

 ..... 20 50 



Vol. XXIII.— No. 1. 5 



