Polarizing Prisms. 361 



and substituting the value /S=5°, this comes to 434 : 39, or 

 about 11 to 1. Thus the average error in the position of the 

 plane of polarization as determined by the new prism will be 

 about one eleventh of that which would be produced by the 

 same errors of adjustment with a Nicol's prism; while the 

 amount of light polarized out of the proper plane will be less 

 than one per cent, of that which would be produced by a Nicol. 

 Again, suppose the prism is turned through an angle co 

 about OX (fig. 6), and let Fig. 6. 



us inquire what is the angle 

 through which the plane of 

 polarization of the emer- 

 gent light is rotated. Let 

 OA' be the new position 

 of the optic axis. Join 

 MA, MA', and in them 

 take points P, P' such that 



MP=MF=|. OP, OP' 



are the directions of vibration for the waves travelling along 

 M in the two positions of the prism respectively. The 

 angle through which the plane of polarization has been turned 

 is P P' or P M P', that through which the prism has been 

 turned is A X A'; and we require to investigate the conditions 

 under which the average difference between these two for all 

 possible positions of M within a certain distance, /3 X say, of X. 



Now we have seen already that if the axis of rotation be at 

 right angles to the optic axis, the average error produced in 

 the determination of the position of the plane of polarization 

 for each of the two positions of the prism will be a minimum; 

 and hence it follows that the average error in the angle be- 

 tween these two positions is a minimum also. 



All these results, of course, hold only for the position of the 

 plane of polarization of the light when in the crystal, and will 

 be modified by the refraction that takes place as the waves 

 emerge into the air. But since the ends of the prism are 

 normal to its length, for all the waves considered the inci- 

 dence is very nearly direct, and the change produced by 

 refraction in the position of the plane of polarization is very 

 small indeed. 



Thus a prism cut as described possesses the following advan- 

 tages over Nicol's prism: — 



1. There is no lateral dispacement in the apparent position 

 of an object viewed through it. 



2. A conical pencil whose axis passes directly through is 

 more nearly plane-polarized than would be the case if the axis of 

 the prism were related to that of the spar in any other manner. 



