OF NEWTON'S RINGS BEYOND THE CRITICAL ANGLE. 657 



light transmitted near the centre increased in intensity till the dark patch disappeared : the patch 

 did not break up into a dark ring travelling outwards. 



On making the analyzer revolve in the contrary direction, the same appearances were of course 

 repeated in a reverse order : a dull central patch was seen, which became darker and darker till it 

 appeared quite black, after which it broke up into a dark ring which travelled outwards till it was 

 lost in the dark field surrounding the spot. The appearance was a good deal disturbed by the 

 imperfect annealing of the prisms. When the plane of incidence was inclined at an angle of about 

 -45" to the plane of primitive polarization, the same appearance as before was presented on revers- 

 ing the direction of rotation of the analyzer. 



28. Although the complete theoretical investigation of the moving dark ring would require a great 

 deal of numerical calculation, a general explanation may very easily be given. At the point of contact 

 the transmitted light is plane polarized, the plane of polarization being the same as at first*. At some 

 distance from the point of contact, although strictly speaking the light is elliptically polarized, it 

 may be represented in a general way by plane polarized light with its plane of polarization further 

 removed than at first from the plane of incidence, in consequence of the larger proportion in which 

 light polarized perpendicularly to the plane of incidence is transmitted, than light polarized in that 

 plane. Consequently the transmitted light may be represented in a general way by plane polarized, 

 with its plane of polarization receding from the plane of incidence on going from the centre 

 outwards. If therefore we suppose the position of the plane of incidence, and the direction of 

 rotation of the analyzer, to be those first mentioned, the plane of polarization of light transmitted by 

 the analyzer will become perpendicular to the plane of polarization of the transmitted light of the 

 spot sooner towards the edge of the spot than in the middle. The locus of the point where the two 

 planes are perpendicular to each other will in fact be a circle, whose radius will contract as the ana- 

 lyzer turns round. When the analyzer has passed the position in which its plane of polarization is 

 perpendicular to that of the light at the centre of the spot, the inclination of the planes of polar- 

 ization of the analyzer and of the transmitted light of the spot decreases, for a given position of the 

 analyzer, in passing from the centre outwards ; and therefore there is formed, not a dark ring 

 travelling outwards as the analyzer turns round, but a dark patch, darkest in the centre, and 

 becoming brighter, and therefore less and less conspicuous, as the analyzer turns round. The 

 appearance will of course be the same when the plane of incidence is turned through 90", so as to 

 be equally inclined to the plane of polarization on the opposite side, provided the direction of 

 rotation of the analyzer be reversed. 



29. The investigation of the intensity of the spot formed beyond the critical angle when the 

 third medium is of a difl'erent nature from the first, does not seem likely to lead to results of any 

 particular interest. Perhaps the most remarkable case is that in which the second and third media 

 are both of lower refractive power than the first, and the angle of incidence is greater than either of 

 the critical angles for refraction out of the first medium into the second, or out of the first into the 

 third. In this case the light must be wholly reflected ; but the acceleration of phase due to the 

 total internal reflection will alter in the neighbourhood of the point of contact. At that point it will 

 be the same as if the third medium occupied the place of the second as well as its own ; at a distance 

 sudicicnt to render the influence of the third medium insensible, it will be the same as if the second 

 medium occupied the place of the third as well as its own. The law of the variation of the accele- 

 ration from the one to the other of its extreme values, as the distance from the point of contact varies, 

 would result from the investigation. This law could be ])Ut to the test of experiment by examining 

 the nature of the elliptic polarization of the light reflected in the neighbourhood of the poini of 



• The rotation oC the plane of jiolarization due to the refraction at the surfaces ai which ihv litthi tnicr» ihc lirsi priMii and quim ihe 

 second is not here mentioned, at it has nothing to do with the phenomenon discunscd. 



