JAMIN ON METALLIC REFLEXION. 7^ 



substance on light ; but if the body, remaining homogeneous, 

 becomes opake, this datum is insufficient, and the modifica- 

 tion undergone by the ray is comphcated by a new influence. 

 Bodies, in fact, never being absolutely opake, give rise to re- 

 fracted waves when they are struck by light, only these waves 

 traverse but a very slight thickness ; we may therefore admit 

 that they are rapidly enfeebled, so as to become insensible at a 

 very small distance compared with the length of an undulation ; 

 and by representing this diminution of energy by a second cha- 

 racteristic, the coefficient of extinction, M. Cauchy seems to 

 have simply translated into a principle that which has been 

 shown to us by experience, and to start from a most reasonable 

 foundation. 



Thus, the formulse which represent the reflexion and refraction 

 of light in transparent bodies depend on one constant only, the 

 index of refraction, and for opake bodies on two given quantities, 

 viz. the index of refraction and the coefficient of extinction. 



In order to deduce from observation the two constants which 

 represent the action of any metal, it will suffice, — 1st, to determine 

 the angle (ij) of maximum polarization : this is the first thing 

 given ; 2nd, to find out the value, at this incidence, of the ratio 



( ^ j of the square roots of the reflected intensities of light po- 

 larized in the plane of incidence and the plane perpendicular to 

 it, and to calculate the angle whose tangent is equal to this ratio : 

 this angle, which we shall call A, is the second given quantity. 



The following are the formulae of M. Cauchy : — J^ and P repre- 

 sent the intensities of the reflected light, polarized in the plane 

 of incidence and in the plane perpendicular to it, that of the 

 incident ray being equal to unity : 



P=tan(4>-45°), J2=tan(x-45°) ; . . . (6.) 

 4> and ^ are given by the formulae 



cot A = cos (2 e — w) sin ( 2 arc tan 73 . ), 



' \ fl-* cos t / 



• /^ , cosi\ 

 cot X = cos u sin I 2 arc tan -y^ I 



(7.) 



(i) represents the angle of incidence; (fl) and(g) are two constants; 

 U and (m) variables which arc calculated as functions of (^), (S) 

 and (i) by the following equations : 



