164 ON THE LIGHT REFLECTED 



oblique ; and, in a plate of varying thickness, the points of maxi- 

 mum difference of phase commence near the middle of an interval, 

 and approach indefinitely to the dark rings as the incidence 

 approaches to 90. 



The tangent of the maximum difference of phase is 



( - 1) (p 2 - 1) 



tan A = 

 or, putting for p 2 its value, 



When n is greater than unity, or the plate denser than the 

 surrounding medium, A = 0, when = 0. As 6 increases, A in- 

 creases continuously; until, when approaches to 90, A approaches 

 indefinitely to the value, 



This is its greatest value. For ordinary flint glass, and for the 

 extreme red ray, ju = 1'60, and A = 26. 



When fi is less than unity, or the plate rarer than the sur- 

 rounding medium, A = 0, when = 0, as before. And A increases 

 as increases, up to the limiting incidence, for which 8 = sin~>> 



and cot A = 2 ^ . The greatest difference of phase, therefore, 



is the same in hoth cases, and in both corresponds to the extreme 

 incidence at which light is admitted into the plate.* 



11. Again, the media being the same on the two sides of the 

 plate, the expressions for the intensities of the two portions of the 

 reflected light, polarized respectively in the plane of incidence and 

 in the perpendicular plane, become 



* It is evident that cot A = 0, and therefore A = 90", when the incidence has 

 either of the values given by the formulas 



tan 1 = , and tan 2 = u 2 * ** 



l-M 2 l-/i*' 



hoth of which are real when the plate is rarer than the surrounding medium. Theee 

 values, however, are both greater than the limiting incidence, and the light dc.es net 

 enter the plate. When the incidence is inteimediate to the two preceding values, A is 

 imaginary. 



