AND TRANSMITTED BY THIN PLATES. 16^3 



the thickness of the plate ; and that, in the phenomena of the 

 rings, it will go through all its values within the limits of a single 

 ring. 



9. The difference, ^ - \> generally vanishes, when sin o = 0,* 



Accordingly, the difference of phase is nothing both at the bright 

 and at the dark rings ; and the light at the former is plane-polar' 

 izt'd. 



The difference of phase is a maximum, when 



tf + w z 



cos a = ^ - ; 

 1 + 2 M? 2 



and denoting by A the maximum value of i// - \, we have 



i* - v? __ 



V/KI-^HI-V)}' 



10. In order to express a and A in terms of the angle of incidence, 

 let us make -- g- = p; and substituting in Fresnel's formulas, we 



find 



sin (9 - &} up - 1 tan(0-y) = /a-p. 



~ sin (0 + 9) ~ W + 1' " tan (0 + tf) ~ /i + p'' 



H being the refractive index for light entering the plate from the 

 surrounding medium. Making these substitutions, the thickness 

 of the plate corresponding to the maximum difference of phase is 

 determined by the formula, 



COS a 



, 



+ fj.- i y 



Or, since p 2 = 1 + (1 - ^} tan 2 0, 



Accordingly, the value of cot ^ increases, from (p + p"*) at a 

 perpendicular incidence, to infinity when the incidence is most 



* When 6 = 90, we have v* = !,; = !; and the expression for ten ty - X ) 

 becomes -, when a = Zmir. It appears from the following, that the difference of 



phase is a maximum in this case. 



M 2 



