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 (i + i'Y 



treated in the same manner, will become 



a (cos ^ - y~^l sin S'), (9) 



if we make 



tan $' = mm', (10) 



tan S' = tan 2' sin ( x - x '), (11) 



1 - sin 2^ cos ( x - x ') > 

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



and here, as before, S' 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 J 



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 = - z . (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 M and x for any metal, when we know its maximum 

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



