192 Lord Rayleigh on Achromatic 



and the retardation in phase is 2t cos a'/X, X being as usual 

 the wave-length in air. 



u The first thing to be noticed is that, when u approaches 

 the critical angle, cos a! becomes as small as we please, and 

 that, consequently, the retardation corresponding to a given 

 thickness is very much less than at perpendicular incidence. 

 Hence the glass surfaces need not be so close as usual. 



" A second feature is the increased brilliancy of the light. 

 But the peculiarity which most demands attention is the 

 lessened influence of a variation in X upon the phase retarda- 

 tion. A diminution of X of itself increases the retardation 

 of phase, but since waves of shorter wave-length are more 

 refrangible, this effect may be more or less perfectly com- 

 pensated by the greater obliquity, and consequent diminution 

 in the value of cos a! '. We will investigate the conditions 

 under which the retardation of phase is stationary in spite of 

 a variation of X. 



" In order that X~ l cos a' may be stationary, we must have 



X sin a! da! + cos a! dX=0, 



where (a being constant) 



cos a! da.' — sin a dp. 

 Thus 



cot 2 a '=--^ (23) 



giving a! when the relation between /uu and X is known. 



" According to Cauchy's formula, which represents the facts 

 very well throughout most of the visible spectrum, 



yu=A + BX- 2 , (24) 



so that 



— i-*^> « 



If we take, as for Chance's t extra-dense flint,' 



B = -984xl0- 10 , 



and, as for the soda-lines, 



p=l-65, X=5-89xl0- 5 , 

 we get 



a' = 79° 30'. 



At this angle of refraction, and with this kind of glass, the 

 retardation of phase is accordingly nearly independent of 

 wave-length, and therefore the bands formed, as the thick- 

 ness varies, are approximately achromatic." 



