Polarizing Prisms. 355 



parallel to M. In practice it is difficult to ensure this; and 

 in general the direction of the wave-normal relatively to the 

 optic axis will be changed, and may now be ON say. But 

 since the planes of polarization of the waves along M and 

 N are different, the angle through which the prism has been 

 turned will not be the angle through which the plane of pola- 

 rization of the incident light has moved. 



Now Nicol's prism is so cut that the angle between the 

 planes of polarization of two waves inclined to each other at 

 but a small angle as they traverse the crystal is considerable. 

 If, then, a slightly conical pencil traverse the prism, the angles 

 between the planes of polarization of the different waves are 

 considerable; or if a parallel pencil traverse the prism inclined 

 at but a small angle to the axis of rotation, and the plane of 

 polarization of this beam be rotated, that rotation will differ 

 considerably from the angle through which the prism has to 

 be turned to reestablish blackness. 



In our figure the wave along M is polarized in a plane 

 at right angles to P, that along ON in a plane at right 

 angles to Q. Consider now a conical pencil of wave-nor- 

 mals in air: it is clearly impossible for it to be plane-polarized, 

 if by plane polarization we mean that the directions of vibra- 

 tion are parallel to the same line; for we cannot have a series 

 of lines touching a sphere all parallel to the same line. Such 

 a pencil, however, may be said to be most nearly plane-pola- 

 rized when all the directions of vibration are parallel to the 

 same plane ; and this plane will be that which passes through 

 the axis of the pencil and the direction of vibration for the 

 wave-normal which coincides with the axis. For if this be 

 the case, the whole of the pencil can pass unaltered either as 

 an ordinary or extraordinary wave through a piece of spar on 

 which its axis falls normally, provided that the optic axis of 

 the spar be respectively either at right angles to or parallel 

 to the plane in question. Using "plane polarization'' in this 

 sense, we proceed to consider when a conical pencil of given 

 vertical angle travelling in a piece of uniaxal crystal is most 

 nearly plane-polarized. 



Now let M (fig. 3) be the axis of the pencil, and P the 

 direction of vibration for the light travelling along M, and 

 let N be any other wave-normal. According to the above 

 statement, the conical pencil will be most nearly plane-pola- 

 rized if the vibration travelling along N is parallel to the 

 plane POM. If, however, the pencil be travelling in a 

 crystal, it is clearly impossible in general for the displacement 

 along N to be parallel to this plane. For let A be the 

 optic axis ; A lies in the plane MO P. Pass a plane through 



