COLOURS OF THIN PLATES. 73 



The theory of thin plates, as it came from the hands of Young, 

 was however incomplete. It is obvious that the intensity of the 

 two portions of light reflected from the upper and under surfaces 

 of the plate can never be the same, the light incident on the 

 second surface being already weakened by partial reflexion at the 

 first. These two portions therefore cannot wholly destroy one 

 another by interference ; and the intensity of the light in the dark 

 rings should never entirely vanish, as it appears to do when homo- 

 geneous light is employed. M. Poisson was the first to point out, 

 and to remedy, this defect of the theory. It is evident, in fact, 

 that there must be an infinite number of partial reflexions within 

 the plate, at each of which a portion is transmitted ; and that it is 

 the sum of all these portions, and not the two first terms of the 

 series only, which is to be considered in the calculation of the 

 effect. Taking up the problem in this more general form, and 

 employing the formula obtained by himself and Young for the 

 intensity of the light reflected and transmitted at a perpendicular 

 incidence, M. Poisson has proved that at this incidence, and at 

 points for which the thickness of the plate is an exact multiple of 

 the length of half a wave the intensity of the reflected and 

 transmitted lights will be the same as if the plate were suppressed 

 altogether, and the bounding media in absolute contact ; so that 

 when these media are of the same refractive power, the reflected 

 light must vanish altogether, and the transmitted light be equal to 

 the incident.* Fresnel afterwards showed that the result was 

 independent of the expression for the intensity of the reflected 

 light ; and by the aid of the property discovered by M. Arago, 

 namely, that the light is reflected in the same proportion at the 

 first and second surfaces of a transparent plate he extended 

 the conclusion to all incidences.! The general expression of the 

 intensity of the light in any part of the reflected or transmitted 

 rings has been given by Professor Airy.J 



Here, then, we have reached a point with respect to which the 

 two theories are completely opposed. According to both, a cer- 



* " Sur le Phenomcnedes Anneaux Colores." Annales de Chimit, torn. xxii. p. 33 

 M. Poisson has further shown that rings absolutely black will be formed at points 

 corresponding to the bright rings in the ordinary case, when the velocity of propa- 

 gation within the plate is a mean proportional to the velocities in the bounding media. 



t Annales de Chimie, torn, xxiii. p. 129. 



I Math. Tracts, p. 302, &c. 



