60 Laws of Reflexion from Metals. 



Secondly, when the incident light is polarized perpendicu- 

 larly to the plane of reflexion, the expression 



tan (i- - i') 

 tan (t + 0' 



treated in the same manner, will become 



a' (cos V - v/" 1 "! sin S'), (9) 



if we make 



tan i//' = mm', (10) 



tan X = tan 2^' sin ( x - x ') , (11) 



/a = 1 ~ sin W cos ( x - x) . 

 1 + sin 2f cos ( x - x ') ' 



and here, as before, & will be the retardation of the reflected 

 light, and a' the amplitude of its vibration. 



The number M= may be called the modulus, and the 

 m 



angle x the characteristic of the metal. The modulus is some- 

 thing less than the tangent of the angle which Sir David 

 Brewster has called the maximum polarizing angle. After two 

 reflexions at this angle a ray originally polarized in a plane in- 

 clined 45 to that of reflexion will again be plane-polarized in a 

 plane inclined at a certain angle (which is 17 for steel) to the 

 plane of reflexion ; and we must have 



tan - ^. (13) 



a" 



Also, at the maximum polarizing angle we must have 



S' - S = 90. (14) 



And these two conditions will enable us to determine the con- 

 stants H and x for any metal, when we know its maximum 

 polarizing angle and the value of ; both of which have been 



