the Black Spot in Liquid Films. 517 



in a plane at any angle with the plane of incidence. The 

 error due to an incorrect setting will be a minimum when the 

 light is polarized either in or perpendicular to the plane of 

 incidence. 



Airy's formula* expressing the relation between the intensity 

 of the reflected light and the thickness of the film is 



46 2 sin 2 - 



1= —f < 2 > 



(l-£ 2 ) 2 + 4& 2 sin 2 2- 

 where b is the coefficient of reflexion, 

 5, 47i>D cos r 



/j, the index of refraction in the film, and D the thickness of 

 the film. 

 Putting 



A: X 



B = 



2tt/jl cos r 



1-6* 



2b 

 and solving the equation for D, 



D = Asin- 1 B 



1-1 



= Asin -1 BI* = ABI*, approximately 

 (since 



D = ABI i {l+i.iB 2 I-i- } 



and 



B 2 I<*008), 



since in nearly all cases coming into consideration 



I<-004. 

 Therefore from (1) 



D = ABcos0. 



Since 6 is nearly — , it is evident that the thickness D is 



approximately proportional to the complement of 6. 



Method of representing the Results. — Instead of computing 



* Undulatory Theory of Optics, p. 53. 

 Phil Mag. S. 5. Vol. 47. No. 289. June 1899. 2 N 



