F. E. Wright — Measurement of Extinction Angles. 3 



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The intensity I 1 of the emergent wave is then proportional to 

 the square of the amplitude 



I 1 A 2 



The equations (3) above, moreover, show that 



A 2 =A l 2 + A 2 2 + 2A 1 A 2 cos-^^(y 1 -a 1 ) 



On substituting the values of A l and A 2 in this equation, and 

 noting that 



L'TT 



"T 



;- d(y l — a) = l — 2 sin%=- cl (y'-a 1 ; 



we obtain A 2 = cr [cos 2 <£— sin 2(0— (£) sin 20 sin 2 -,- d (y 1 — a 1 )] (4) 



I 1 A 2 

 and finally, y=— 2 = cos 2 <£— sin 2(0 — <£) sin 20 sinVc? (y 1 — a 1 ) (5) 



But the velocity of light Y, period of vibration T,and wave 

 length A., are so related that YT = A, and if we consider the 

 velocity unity, then we may replace T by A, and the equation 

 (o) reads : 



Ti 



T =I 1 = cos 2 <^) — sin 2 (0— <£) sin 20 sin 2 - d (y 1 — a 1 ) 



This is the usual expression for the relative intensity of the 

 emergent waves ; it may, however, be brought into more con- 

 venient form for practical purposes. To save space, let sin 2 



— (y 1 — a 1 ) — K, where K may have any value from to + 1 ; 



then 



I= 1+C 2 OS ^ -Ksm2gsin2(g-^) 



2l i = l + cos 2<£ — 2K sin 20 sin 2(0 — <£) (a) 



= 1 -fcos 2$— K (cos 2<£ (1— cos 40) — sin 2<f> sin 40) (b) 

 = 1 + (1— K) cos 2cf> + K cos 2(cf> — 20) (6) 



For a given angle 9 to find the condition that the intensity 

 will be zero, the equation (a) of the foregoing can be changed to 



2l ] = l + (l — 2K sin 2 20) cos 2<f> + 2K sin 20 cos 20 sin 2<£ 

 = 1+K 1 cos 2c£ + K 2 sin 2</> (7) 



in which 



K=l — 2K sin 2 20 and K„=2K sin 20 cos 20. 



