528 Mr. A. E. Oxley on an Apparatus for the 



the azimuth of the incident vibration with respect to the 

 latter so that the beam of plane-polarized light alter passing 

 through it would be circularly polarized. 



(2) By Calculation. — The new azimuth can be determined 

 more accurately by calculation. Consider the layer of air 

 forming the joint. Let (f> be the angle of incidence in the 



Fig. 4. 

 air 



y?ecss 



glass (fig. 4), (// the angle of* refraction. The ratio of the 

 refracted amplitudes in the air-gap is 



2 sin 4>' ■ cos <f> sin (<£ + <£') cos (<fi— </>') _ ,. ,,n 

 sintf + tf/) * 2 sin <f>' cos <j> ~ <*>*&- 9 )> 



the azimuth of the incident vibration being 45°, After the 

 second refraction this ratio is 



COS 2 (0-0O . 



If we make the azimuth of the incident vibration X2 

 where 



1 



tan O = 



cos" j <p — arc. sm (/* sin <j>) } ' 



n being measured from the edge AB (fig. 3), the trans- 

 mitted amplitudes will be equal, and since their phase- 



difference is still — , the emergent beam of light will be 



circularly polarized. Using the known values of <£ and /i, 

 we find 



a = 49° 2'. 



An estimation of the ellipticity of the orbit corresponding 

 to any value of dA = £ (^ay), can be obtained as follows, 

 Let the transmitted components be represented by the 

 equations 



x = r . cos wt, y = r sin (wt + £), 



The equation of the orbit is 



* 2 (l-K 2 ) 



± 2 ^ + ^ = ±> 



