268 ON THE REFLEXION AND REFRACTION OF LIGHT. 



= ft 2 -- - , i.e., when tan (0 + 0,) = <*> , 



which agrees with experiment, and this minimum value is, since 



(27) gives - = n, 

 u 



f? V-V-2 ^_ IY 



'' }< 



If jj, = - , as when the two media are air and water, we get 

 3 



F 1 . 

 _ 2 = nearly. 



It is evident from the formula (28), that the magnitude of 

 this minimum value increases very rapidly as the index of 

 refraction increases, so that for highly refracting substances, 

 the intensity of the light reflected at the polarizing angle be- 

 comes very sensible, agreeably to what has been long since 

 observed by experimental philosophers. Moreover, an inspec- 

 tion of the equations (25) will shew, that when we gradually 

 increase the angle of incidence so as to pass through the polar- 

 izing angle, the change which takes place in the reflected wave 

 is not due to an alteration of the sign of the coefficient /3, but 

 to a change of phase in the wave, which for ordinary refract- 

 ing substances is very nearly equal to 180 ; the minimum value 

 of /3 being so small as to cause the reflected wave sensibly 

 to disappear. But in strongly refracting substances like dia- 

 mond, the coefficient /3 remains so large that the reflected 

 wave does not seem to vanish, and the change of phase is con- 

 siderably less than 180. These results of our theory appear to 

 agree with the observations of Professor Airy. (Camb. Phil. 

 Trans. Vol. IV. p. 418, &c.) 



Lastly, if the velocity 7, of transmission of a wave in the 

 lower exceed 7 that in the upper medium, we may, by suf- 

 ficiently augmenting the angle of incidence, cause the refracted 

 wave to disappear, and the change of phase thus produced in the 



