26 Mr. O'BRIEN ON THE REFLEXION AND REFRACTION OF LIGHT, &c. 



11 4 



Let us suppose, at a venture, that the value of m is — for glass, and - for diamond : then the 



value of ( "' ~ ^" l is about — for glass, and — for diamond ; therefore we have 

 \ir + \) 100 15 



o^ = for glass, 



' 600 ^ 



a' = — for diamond. 

 15 



These expressions, if correct, would indicate that the reflected ray was scarcely visible for glass ; 

 and faint, though decidedly visible, for diamond : which, I believe, is the case. From this example 



it is clear that if we suppose the normal index of refraction to be less than about — when the 



transversal index is less than -, the reflected ray at the polarizing angle will be scarcely visible 



for plate-glass and substances of lower refractive power : and if we suppose the normal index not 



less than about - when the transversal is greater than 2, the reflected ray will be decidedly visible. 

 3 



Supposing this to be true, - >j' will be very small for substances of moderate refractive power, 

 and therefore Fresnel's formulae will hold for such substances, at least the deviation from Fresnel's 

 formulae will be insensible. 



Hence, for substances of moderate refractive power m will be always small ; but \{/, and there- 

 fore the phase (to + \//) will increase rapidly by very nearly 180" while the angle of incidence is 

 passing through the polarizing angle; this is evident from (l). 



For substances of high refractive power, - tj' will not be very small ; therefore there will be 

 a sensible deviation from Fresnel's formulae. Moreover w will not be very small, and \f,, and 

 therefore the phase ((« + >//) will increase by a quantity somewhat less than 180", while the angle 

 of incidence is passing through the polarizing angle. 



These results are in strict accordance with the experiments of Mr Airy ; see the Cambridge 

 Transactions, Vol. iv, p. 422. 



