35 J: F. E. Wright — Measurement of Extinction Angles. 



of the plate and the plane of the incident vibrations, the 

 equations for the resultant waves are 



A A • 2lrt 1 



x=u cos 6= a cos 6 sin — and y=ic sm 



a sm v sm 



27rt 

 T 



Each of these vibrations traverses the plate with a different 

 velocity and the time required by the fast wave to traverse the 

 plate of thickness d will be t x = d.a\ while the time required 



by the slow wave is t 2 = d.y 1 where a 1 and 7' are respectively 

 the refractive indices of the two waves. On emergence, 

 therefore, the equations for the periodic displacements will be 



x 1 = a cos sin j= (t—da 1 ) and v l = a sin sin — (t—dy 1 ) 



On reaching the upper nicol each of these vibrations is again 

 resolved further into two component vibrations again normal 

 to each other, one of which, however, is annulled by total 

 reflection. If $ be the angle between the principal planes of 

 the nicols, then the component vibrations emerging from the 

 upper nicol are . 



27T 27T 



$=x l cos (6— <f>) = a cos(0— <£)cos0sin-=- (t — da 1 ) = A i sin — (I — da 1 ) 



2tt 2tt 



rj=y 1 sin (0— <£) = asin(0— <£)sin0sin- f - (t—dy 1 )=A 3 sm 7^ (t—dy 1 ) 



and the resultant amplitude 



A = ^ + 7 7 =A 1 sin^ r (t — da 1 ) -f A s sin^ (t— dy 1 ) 



