186 



FRANCIS DEAS ON THE SPECTRA FORMED BY THE PASSAGE OF 



the axis of x ; and let this crystal produce a retardation whose phase is p in 

 the light polarised in the plane of the axis 



parallel to axis x' — c cos a cos {nt + p) 



perpendicular to axis y' — c sin a cos nt . 



Next, let the light fall on an analyser in a plane inclined yS to the axis of 

 the crystal. The analysed light will be 



x" = c cos a cos /3 cos (nt + p) + c sin a sin /3 cos nt . 



The intensity of this light will be 



c 2 {cos 2 a cos 2 /3 + sin 2 a sin 2 /3 — 2 sin a cos a sin /3 cos /3 cos p\ 



or g c 2 1 1 + cos 2a cos 2/3 — sin 2a sin 2/3 cosj? j . 



We may represent this whole process geometrically as follows : — 



Let OCO' represent the original polarised 

 light, OCA the angle between the plane of 

 polarisation and the axis of the crystal. 

 The light is resolved into ACA' and DCD'. 

 Now, let a semicircle be drawn with radius 

 OA, and let OAp — p be the phase of retar- 

 dation ; draw pT perpendicular to AO, and 

 draw an ellipse with centre C and touching 

 AO in T and also the other sides of the 

 parallelogram. This ellipse is the path of the 

 light emergent from the crystal. Now let BCB' be the plane of the analyser. 

 Draw Tb T'b' tangents to the ellipse perpendicular to BB 7 , then bCb' represents 

 the amplitude of the emergent light. 



The result of the process may be made still simpler thus : 



Draw CO = c, in the plane of polarisation, CA parallel to 

 the axis of the crystal, and CB parallel to the analyser. 

 Draw OA perpendicular to CA, AB to CB, and OD to CB, 

 then CB = c cos a cos /3, and BD = c sin a sin (3 ; make DBP =p, 

 the phase of retardation, and BP = BD. Then CP represents 

 the amplitude of the emergent light. 



The emergent light will be either a maximum or a 

 minimum when p = 0° or nir. 



The minimum will be zero, or blackness, only in the following cases, 



1. When a + /3 = \ and p = or 2mr. 



2. When a — /3 = \ and p = (2ra + l)n. 



