336 On Polarization of Light by Refraction. 



The case, however, is different with the retracted light. The 

 value of Q' has one minimum at 0° and another at 90°, while its 

 maximum is at 78° 7', while the force has its minimum at 0° and 

 its maximum at 90°, where its effect is a minimum only because 

 there is no light to polarize. At the incidence of 78° 7', where the 

 quantities Q, Q', reach their maxima, the reflected light is exactly- 

 one half of the transmitted light; sin='9 = cos=^<p and tan 9'= cos 9. 



At 85° 50' 40'', where the transmitted light is one half of the 

 reflected light, the deviation («" — i')=-45°, and the quantity of po- 

 larized light is one third of the transmitted light, one sixth of the re- 

 flected light, and one ninth of the incident light. Sin^cp' : 003^9 = 

 reflected light t transmitted light, and cot 9'= sin {i — i'). 



At 45° we have (i+i') + (i-i') = 90° and cp'={i-i'), 



^ cos (i-\-i') , ,. .. (sin(^ — i'))- 

 Tan (t — i')= r-' — v\' and tan-(» — i')^ = r-^ — r-~r^7TTi 



At 56° 45', the polarizing angle, the formula for reflected light 

 becomes R=^(sin2(i — i'))^ ; but at this angle we have ^'=90° — i. 

 Hence we obtain the following simple expression in terms of the an- 

 gle of incidence, for the quantity of light reflected by all bodies at 

 the polarizing angle. 



R=^(cos2i)^ 



I have already mentioned the experiment of M. Arago with plates 

 of glass, in which he found that " at every possible inclination" the 

 quantity of light polarized by transmission was equal to the quantity 

 polarized by reflexion. This conclusion he extends to single surfa- 

 ces ; but it is remarkable that the law is true of single surfaces in 

 which he did not ascertain it to be true, while it is incorrect with re- 

 gard to plates in which he believes that he has ascertained it to be 

 true. As the consideration of this point does not strictly belong to 

 the present branch of the inquiry, I shall reserve it for a separate 

 communication, " on the action of the second surfaces of transpa- 

 rent plates upon light."* 



Allerly, December 29, 1829. 



** Inserted in the last number of this Journal. 



