AND REFRACTION OF LIGHT.. 23 



= /u 2 , i. e., when tan (9 + 9) — to , 



Co 



which agrees with experiment, and this minimum value is, since (27) 



b 

 gives - - M , 



£-, (w } " 2 0'-> v (28) . 



4(/u + 1) fx* + (m - 1) -| 



4 

 If /u. = - , as when the two media are air and water, we get 

 3 



- = — nearly. 



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

 minimum value increases very rapidly as the index of refraction in- 

 creases, so that for highly refracting substances, the intensity of the 

 light reflected at the polarizing angle becomes very sensible, agreeably 

 to what has been long since observed by experimental philosophers. 

 Moreover, an inspection of the equations (25) will shew, that when we 

 gradually increase the angle of incidence so as to pass through the po- 

 larizing angle, the change which takes place in the reflected wave is not 

 due to an alteration of the sign of the coefficient (5, but to a change 

 of phase in the wave, which for ordinary refracting 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 sub- 

 stances like diamond, the coefficient /3 remains so large that the re- 

 flected 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. (Comb. 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 sufficiently augment- 

 ing the angle of incidence, cause the refracted wave to disappear, and 

 the change of phase thus produced in the reflected wave may readily 

 be found. As the calculation is extremely easy after what precedes, it 



