On the Intensity of the Light reflected from a Pile of Plates. 487 



The intensity of the light reflected from an infinite number of plates, 

 as we see from (18), is a -1 ; and since a is changed into a -1 by 

 changing the sign of a or of A, 



a- 1 =V(l+f*-< l -A) > (21) 



Zr 



which is equal to 1 in the case of perfect transparency. Accordingly 

 a substance which is at the same time finely divided, so as to present 

 numerous reflecting surfaces, and which is of such a nature as to be 

 transparent in mass, is brilliantly white by reflected light, — for 

 example snow, and colourless substances thrown down as preci- 

 pitates in chemical processes. 



The intensity of the light reflected from a pile consisting of an 

 infinite number of similar plates falls off rapidly with the transpa- 

 rency of the material of which the plates are composed, especially at 

 small incidence. Thus at a perpendicular incidence we see from the 

 above Table that the reflected light is reduced to little more than one 

 half when 2 per cent, is absorbed in a single transit, and to less than 

 a quarter when 10 per cent, is absorbed. 



With imperfectly transparent plates, little is gained by multiplying 

 the plates beyond a very limited number, if the object be to obtain 

 light, as bright as may be, polarized by reflexion. Thus the Table 

 shows that 4 plates of the less defective kind reflect 79 per cent., 

 and 4 plates of the more defective as much as 94 per cent., of the 

 light that could be reflected by a greater number, whereas 4 plates 

 of the perfectly transparent kind reflect only 60 per cent. 



The Table shows that while the amount of light transmitted at the 

 polarizing angle by a pile of a considerable number of plates is mate- 

 rially reduced by a defect of transparency, its state of polarization is 

 somewhat improved. This result might be seen without calculation. 

 For while no part of the transmitted light which is polarized perpen- 

 dicularly to the plane of incidence underwent reflexion, a large part 

 of the transmitted light polarized the other way was reflected an even 

 number of times ; and since the length of path of the light within 

 the absorbing medium is necessarily increased by reflexion, it follows 

 that a defect of transparency must operate more powerfully in redu- 

 cing the intensity of light polarized in, than of light polarized perpen- 

 dicularly to the plane of polarization. But the Table also shows that 

 a far better result can be obtained, as to the perfection of the polari- 

 zation of the transmitted light, without any greater loss of illumination, 

 by employing a larger number of plates of a more transparent kind. 



Let us now confine our attention to perfectly transparent plates, 

 and consider the manner in which the degree of polarization of the 

 transmitted light varies with the angle of incidence. 



The degree of polarization is expressed by the ratio of ^ to >L, 

 which for brevity will be denoted by x« When ^=1 there is no 

 polarization; when x = the polarization is perfect, in a plane per- 

 pendicular to the plane of incidence. Now \p (which is used to 

 denote \p x or \p 2 as the case may be) is given in terms of p by one 

 of the equations (20), and p is given in terms of i—i 1 and i+i 1 by 



