22 Mb. O'BRIEN ON THE REFLEXION AND REFRACTION OF LIGHT 



arrive at exactly the same expressions as before, for V^ and V, with this difference, that 



_ . „ . 2 a cos o) . 1 i- „ 



coefficient of V is instead of 2acosai. 



This is exactly the second case considered in Airy's Tracts, p. 361. 



SECTION V. 



JVhu Normal Waves never produce any sensible Effect on the Eye directly or 



indirectly. 



(25.) We must suppose of course that normal waves cannot produce vision directly, (?". e.) 

 that when such waves are incident on the retina they do not affect the optic nerve in such a manner 

 as to give rise to the sensation of light. But we have proved that when a transversal ray 

 undergoes oblique refraction it brings into existence normal rays, and it would be easy to shew 

 that, in the same manner, the oblique refraction of a normal ray will produce transversal rays. 

 Therefore, though normal waves cannot affect the retina directly, they may do so indirectly, 

 by giving rise to transversal waves. Now it is a matter of fact that they do not produce this 

 indirect effect, and it therefore becomes necessary to explain theoretically why they do not. 



(2(5.) If we take the hypothesis in Article (20), it is easy to do this. For suppose the 

 normal ray, generated by the oblique refraction of a transversal ray at the first surface of a prism 

 or lens, to fall on the second surface at an angle of incidence sin"'p, and let the transversal 

 ray produced by this oblique refraction emerge at an angle sin~'p', then, as in Article (l9), we 



may shew that ^ = — , and therefore p' = -y, p. Now by our hypothesis ~j-, is very large, 



therefore, unless p is very small (in which case the transversal ray will not be produced at 

 all), p will be >1, and «' impossible; i.e. the transversal ray will be extinguished. (See 

 Article 23). 



Thus the normal waves generated by the first refraction, will not produce transversal waves 

 at the second refraction. 



Again, if we take the hypothesis in Article (21), and assume moreover that v" and v,^ 

 are large compared with v and v, it is easy to see, by similar reasoning, that the normal rays 

 will be extinguished immediately after their production by the first refraction. 



It is evident, therefore, that on either hypothesis (adding to the latter, that v^ and v" are 

 large compared with v and t''), normal waves will produce no sensible effect on the eye, even 

 indirectly. 



SECTION VI. 



Whether Polarized Light con.nsts of Vibrations at Right Angles to, or Parallel 



to the Plane of Polarization. 



(27) Theee can be no doubt of the truth of Sir D. Brewster's law of tangents, and 

 the laws of the rotation of the plane of polarization given by M. Arago, and Sir D. Brewster. 

 From these laws we shall attempt to prove, that polarized light consists of vibrations perpen- 

 dicular to the plane of polarization, in the following manner. 



