14 L. B. Tuckerman 



The. total intensity of the light =2/*; 



The ellipticity e, the ratio of the minor and major axes of the 

 ellipse. The ellipticity is considered positive when the light vec- 

 tor rotates counter clockwise, as we look in the direction of prop- 

 agation of the light 



P—VP—S 2 , s 



'=- ^ — (23) 



The positive sign of the square root is always taken so that 

 — i<V<+r. 



The following inverse relations are also useful : 



2p=i+j=i m +y m 



1—e 2 



2 0=1— J— ( / — / ) COS 2 0=2 P — -z COS 2 6 



. — i—e- 



2K=2^ I J cos<l>=(/ m —/ m ) sii\26=2P — ■ — 7, sin 2 



i-\~e 



s=vij sin 4>=y'u=P^ 



It is often convenient to express the ellipticity in terms of an aux- 

 iliary angle, w, defined by the equation, tgw=<?. Then 



1 — e 1 2c . . 2e 



— : — 5=cos2w, — ■ — ^=sin2w and =to'2w 



i-\-e* \A r e i 1 — <r 



from which: 



Q=P cos 2 o) cos 2 8 



K=P cos 2 wsii\2 6 (25) 



S=-Psin2w 



The equation 



5. The Poincare Sphere 



Q+Zf+S^P 2 (18) 



suggests a geometric representation of the quantities involved. 

 Letting Q, K and 5 represent the distances of a point from the 



170 



