328 CLAUSIUS ON THE BLUE COLOUR OP THE SKY 



the formulae, both colours must be complementary, inasmuch as 

 we have 



We will first turn our attention to the reflected light, assuming 

 the incident light to be white. 



The intensity of the single colours, if the corresponding in- 

 tensity of the incident light be denoted by d^, can vary between 

 the limits 



Assuming, in the first place, the thickness of the plate as so in- 

 considerable that it exactly amounts to a quarter of an undula- 

 tion of the extreme violet, and let the light be supposed to fall 

 perpendicularly, by which we shall have cosi'=l ; then for the 



violet rays sin^ ( 27r — r-7 — j becomes sin^ ( — j = 1^ and the re- 

 flexion of these rays is thus the greatest possible. The other 

 rays, on the contrary, will be the less reflected the greater their 

 wave-lengths ; and the mixture of all gives a whitish-blue. If 

 the light falls obliquely on the same plate, so that cos i' should 

 be <1, the violet would no longer undergo its maximum re- 

 flexion, while the other circumstance would remain unchanged, 

 that all the remaining rays would be still less reflected, the dif- 

 ference increasing as the wave-lengths diminish. The total 

 light would be therefore weaker, but still blue. 



This latter phaenomenon must continually take place when 

 the thickness of the plate is still less than that assumed above. 

 The reflected light must appear as a darker and darker blue, 

 until the plate becomes too thin to reflect light at all, a result 

 which is obtained from the simple consideration of the rings of 

 Newton, where blue is the first colour which surrounds the 

 black centre. 



Let us, on the contrary, suppose that the thickness of the plate 

 becomes gradually greater than that assumed above, the violet 

 will be more feebly reflected, and instead of it some other colour 

 will undergo its maximum reflexion, and so the tint of the 

 whole light will be changed. As the thickness increases we 

 obtain the series of colours observed in Newton's rings, namely, 

 blue, white, yellowish white, orange, red, violet, blue, &c. 



