Light from a Dense to a Rarer Medium. 347 



For this equation to admit of a real solution, yS must be 

 equal to, or less than, unity. When y ' = 1 no refraction 

 takes place ; when fjj is less than unity, the medium traversed 

 by the incident ray is optically denser than that on the 

 further side of the refracting surface. If y is the index of 

 refraction from the second to the first medium, then the 

 critical value of i is given by the equation 



. . , 1 

 smi = a = — 



A very simple explanation of this result is afforded by the 

 Wave Theory of Light. The more salient features of the 

 problem have received ample attention ; but it happens that, 

 in a certain direction, the theory has not been followed to its 

 logical conclusion, with the result that a phenomenon, some- 

 what paradoxical from the ordinary point of view, has 

 escaped observation. This circumstance will, we hope, afford 

 an excuse for a brief preliminary consideration of the Wave 

 Theory, as far as applies to the refraction of light from a dense 

 to a rarer medium. 



According to the Huyghens-Fresnel theory of wave- 

 propagation, each point of a wave-surface must be considered 

 as a separate source of disturbance, whence originates a 

 secondary wavelet, which is spherical if the medium is iso- 

 tropic, and which enlarges at a rate dependent only on the 

 nature of the medium. After any lapse of time the new 

 wave-front is formed by the mutual reinforcement of the 

 various secondary wavelets ; at points where reinforcement 

 does not occur, destructive interference takes place. Further, 

 when a wave is incident on the interface between two 

 different media, each point of the interface becomes a source 

 of disturbance as the incident waves sweep past. At each 

 of these points two secondary wavelets originate : one spreads 

 outwards into the medium beyond the interface, while the 

 other spreads out into the medium containing the incident 

 wave. The reinforcement of the wavelets propagated in the 

 medium containing the incident wave gives rise to the 

 reflected wave-front. The wavelets propagated in the medium 

 beyond the interface may or may not be able to reinforce 

 each other, with the result that a refracted wave may or may 

 not be formed, according to circumstances. If no refracted 

 wave is formed, the secondary wavelets in the medium 

 beyond the interface destructively interfere with each other 

 throughout that medium ; but in all cases secondary wavelets 

 are formed in each of the media separated by the interface. 



2 A2 



