460 HISTORY OF OPTICS. 



a right angle with the plane of reflection ; for the 

 quantities of the oppositely 12 polarized light in such 

 an incident ray are equal, as they are in common 

 light; but the relative quantities of the oppositely 

 polarized light in the reflected ray are indicated by 

 the new plane of polarization ; and thus these rela- 

 tive quantities become known for the case of com- 

 mon light. The results thus obtained were also 

 confirmed by facts; and in this manner, all that 

 was doubtful in the process of Fresnel's reasoning, 

 seemed to be authorized by its application to real 

 cases. 



These investigations were published 13 in 1821. 

 In succeeding years, Fresnel undertook to extend 

 the application of his formulae to a case in which 

 they ceased to have a meaning, or, in the language 

 of mathematicians, became imaginary ; namely, to 

 the case of internal reflection at the surface of a 

 transparent body. It may seem strange to those 

 who are not mathematicians, but it is undoubtedly 

 true, that in many cases in which the solution of a 

 problem directs impossible arithmetical or algebra- 

 ical operations to be performed, these directions 

 may be so interpreted as to point out a true solution 

 of the question. Such an interpretation Fresnel 

 attempted 14 in the case of which we now speak; 



13 It will be recollected all along, that oppositely polarized 

 rays are those which are polarized in two planes perpendicular 

 to each other. See p. 375. 



13 An. Chim. t. xvii. u Bullet, des. Sc. Feb. 1823. 



