547 



absorption in a single transit. The light reflected by a plate will be 

 made up of that which is reflected at the first surface, and that which 

 suffers 1, 3, 5, &c. internal reflexions. If the intensity of the inci- 

 dent light be taken as unity, the intensities of these various portions 

 will be 



and if r be the intensity of the reflected light, we have, by summing 

 a geometric series, 



. rt _i_0 'P) 2 ?^ 1 (4} 



~ P~r 22* y*f 



Similarly, if t be the intensity of the transmitted light, 



! fV 

 and we easily find 



which is in general less than 1, but becomes equal to 1 in the limiting 

 case of perfect transparency, in which case y=l. 



The values of /u, , and q in any case being supposed known, the 

 formulae (I), (2), (3), (4), (5) determine r and t, which may now 

 therefore be supposed known. The problem therefore is reduced to 

 the following : There are m parallel plates of which each reflects 

 and transmits given fractions r, t of the light incident upon it : light 

 of intensity unity being incident on the system, it is required to find 

 the intensities of the reflected and refracted light. 



Let these be" denoted by $(m\ $(m). Consider a system of m + n 

 plates, and imagine these grouped into two systems, of m and n plates 

 respectively. The incident light being represented by unity, the 

 light <l>(m) will be reflected from the first group, and i//(m) will be 

 transmitted. Of the latter the fraction *//() will be transmitted by 

 the second group, and (j>(ri) reflected. Of the latter the fraction 

 I//OM) will be transmitted by the first group, and <j>(ni) reflected, and 

 so on. Hence we get for the light reflected by the whole system, 



and for the light transmitted, 



