Second Surface of a Thin Plane Parallel Plate. 21 



produced in the electric vector perpendicular to the plane of 

 incidence ; and by the reciprocal property of 3 lax weir's 

 equations the above discussion holds for this electric vector, 

 if we interchange K and /jl. 



— tan—/? =\/ J+-- J- cot(/3 — L), 



2 l V lv 2/C x 1 cos </> 2 K ^ n 



where a looser, 

 tan /3 = f — " . 



COS^o fl 3 V s 



Hence putting /i=l, and writing A p — A S = A, we have 



A X /geot(.-L)- A /|cot(^-L) 



— = arc tan , — j— , (5) 



2 COSd> 2 , , T\ 4-/0 T\ C0S 9l 



— T + cot (a — L) cot f/3 — L) ; 



COS <p i COS <p 2 



where . /Ko cos <h - ; 



tan « =•• « A / T^" r~ 



V K 3 cos<£ 2 



and . . /K 3 cos <£., 

 tan # = 2 a / |7 -r • 



V K 2 cos<£ 2 



This formula gives the relative phase-difference for any 

 angles of incidence, when /, the thickness of the plate, is 

 known. To find I in terms of A, i.e. to find the thickness of 

 the film from the observations, put <r=« — L. y = (3 — L. 

 Then 





Vk; cos *-\/§ 



cot y 



tan= = " " x v ^ 2 





cos 2 cos 4> t 



— r- -f cot a? cot ?/ 

 cos 9, *■ cos ©.-> 



\/§ cos ' r sin y-^^ cosy sin., 



cos d)o . . cos d>i 



~ sin cT sm y + r r cos x cos y 



cos <p! ° cos <£ 2 



^^ ( cos (*?-#)- cos (# + y)) + 



COS 0, \ / cos 92 \ / 



J /K, /Ka . , / /K 2 , /Ka 



= s»n(.r + y)^y K ; ~ a/ g-J - sm (g- y) ^/ g- + ^/ g-j 



v ^^Vcosc^o cos^/ v ^ \COS<£ 2 COS pi/ 



