232 On Polarization of Light by Refraction. 



Fres 



transm 

 T=l- J 



Now since by Fresnel's formula the quantity of reflected light is 

 sin 2 {i — i') tan^' (» — *0\ 

 sin^ (i+*0 tan= {i+i')l 

 the quantity of transmitted light T will be 



sin 2 {i-i') tan 2 (i-i') 



^sin^ (i+i')"^tan2 (i+i') 

 Hence 



^ \ ^\sin=^ (i+i')^ tan^ (i-fi')//\^~^l + (cos(i-iO)' / 

 This formula is applicable to common light in which cot x=l dis- 

 appears from the equation ; but on the same principles which we 

 have explained in a preceding paper, it becomes for partially polari- 

 zed rays and for polarized light, 



/ /sin^ (i-i') tan^ {i-i') \\ 



Q^=-ll-Mc ;n-' r ■ •/( cos= X + , , /• , -a sin^ x] ) 

 \ \sm- (i+z) lan^ (» + * ) // 



(cot a? cos (i — i'))' 



1—2 ^ '^:: 7-^ — 



1 + (cot X cos (* — «')) ^ 



In all these cases the formula expresses the quantity of light real- 

 ly or apparently polarized in the plane of refraction. 



As the planes of polarization of a pencil polarized +45° and 

 — 45° cannot be brought into a state of coincidence by refraction, 

 the quantity of light polarized by refraction can never be mathemat- 

 ically equal to the whole of the transmitted pencil, however numer- 

 ous be the refractions which it undergoes ; or, what is the same 

 thing, refraction cannot produce rays truly polarized, that is, with 

 their planes of polarization parallel. 



The preceding analysis of the changes produced on common 

 light, considered as represented by two oppositely polarized pencils, 

 furnishes us with the same conclusions respecting the partial polari- 

 zation of light by refraction, which we deduced in a preceding pa- 

 per respecting the partial polarization of light by reflexion. Each 

 refracting surface produces a change in the position of the planes of 

 polarization, and consequently a physical change upon the transmit- 

 ted pencil by which it has approached to the state of complete po- 

 larization. 



This position I shall illustrate by applying the formula to the expe- 

 riments which I have published in the Philosophical Transactions 

 for 1814. 



According to the first of these experiments, the light of a wax 

 candle at the distance of ten or twelve feet is wholly polarized by 



