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XLIII. On the Laws of Reflexion and Refraction at the Sur- 

 faces of Substances of High Refracting and Absorbitig PowerSf 

 such as Metals. By the Rev. M. O'Brien, late Fellow of 

 Caius College, Cambridge^ and Professor of Natural Philo- 

 sophy and Astronomy in King^s College, London. 

 [The subject resumed from p. 123.] 

 To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



1. TN a former communication I mentioned that I had in- 

 ^ vestigated the laws of reflexion and refraction at the 

 surface of a transparent substance, the particles of which are 

 supposed to resist the vibrations of the aethereal fluid ; I shall 

 now briefly state and prove these laws, and show how they 

 may be tested by experiment. In a memoir printed in the 

 Cambridge Transactions, vol. viii. p. 7, I have obtained cer- 

 tain results*, which, if true, show the great importance of 

 taking properly into account the normal as well as the trans- 

 versal waves, in investigating the laws of reflexion and refrac- 

 tion. These results, as well as the notation and method em- 

 ployed in that memoir, I shall now make use of without further 

 explanation. The waves are supposed to be plane waves, and 

 the refracting surface is also supposed to be plane. 



2. The following are the laws of refexion and refraction 

 for y'^x^ixGUS, perpendicular to the plane of incidence. 



Let the general expression for the incident disturbance be 

 a cos {n t — k [px + sz) }, 

 the refracting surface being taken as the plane oi xy, and the 

 plane of incidence as the plane oi x z\ p and s being the sine 

 and cosine of the angle of incidence, which angle we shall 

 denote by the letter <fi. 



Then the general expression for the reflected disturbance 

 will be (as we shall presently prove), 



— P « cos \nt — h{j) X — s%) — fl }; 



and the expression for the refracted disturbance will be 



rte-*A;^|cos {nt—k{px-\-(Jz))—VQ.o'i>{nt—'k[jpx-\-(yz) — ^) |. 



* I shall just state one of these results, to show the importance of taking 

 into account the normal waves. If a- be the intensity of a ray incident on 

 a surface of high refractive power, the intensity of the reflected ray, when 

 the tangent of the angle of incidence is ^, will be 



I*, being the index of refraction for transversal waves, and j/that for normal. 

 This remarkable result fully explains the peculiarities of reflexion at highly 

 refractive surfaces (see the Memoir, p. 2G). 



