( 393 ) 



XX. — On FresneVs Formula^ for the Intensity of Reflected aiid Refracted Light. 

 By Philip Kelland, M. A., late Fellow of Queen's College, Cambridge, Profes- 

 sor (f Mathematics, Sfc, in the University of Edinburgh. 



Read February 18. 1839. 



INTRODUCTION. 



It is well known, that when light is incident on a refracting surface, a por- 

 tion of it is reflected, whilst both the transmitted and the reflected light undergo 

 polarization. The obvious mode of accounting for this, is to attribute to the par- 

 ticles on whose motion light is supposed to depend, the property of transmitting 

 one class of vibrations more freely than another, limited, however, by the direc- 

 tion and mode of action of the adjacent particles. M. Fuesnel, in order to deter- 

 mine the intensity of light reflected and refracted under different circumstances, 

 assumed that the density of the particles of ether is greater in refracting media 

 than in vacuo. By means of this assumption, and other subsidiary ones, he de- 

 duced foraiulse for the intensity of the reflected and refracted light, by means of 

 which the amount of polarization, as weU as the change Avhich the plane of pola- 

 rization undergoes, can be readily deduced. The obvious interpretation of the 

 formulae coincided precisely with discoveries which had been long known, and the 

 more difficult deductions from them have been tested by numerous experiments 

 of Sir David Brewster and others. It appears that, although for highly refrac- 

 tive media, they may be only approximations, yet, in most cases, they are so 

 close as to deserve the most careful attention of those who endeavour to establish 

 a correct mechanical theory. 



M. Cauchy, in different memoirs, has laboured to deduce M. Fresnel's for- 

 mulae from the equations of motion, and, in one instance, from assumed condi- 

 tions of a nature not widely different from M. Fresnel's own. The fact that 

 these expressions had been deduced from the assumption of a greater density 

 within refracting media than without, appeared to throw a doubt over the truth 

 either of the molecular hypothesis, which seemed to require the reverse, or of the 

 formulae themselves. 



Whilst M. Cauchy is tossed about with various and conflicting conclusions, 

 Mr M'CuLLAOH is led, by totally different considerations, to one of the most im- 

 portant of them, viz. that the vibrations which constitute light polarized in the 

 plane of incidence are vibrations effected in that plane, a result which is direct- 



VOL. XIV. PART II. 3 H 



