Light from a Dense to a Rarer Medium. 349 



which determines the direction AP in which the disturbance 

 travels in the upper medium. 



When fAsmi=l 9 0—-^, and the disturbance travels along 



the surface AC. When /jl sin i > 1, no value o£ can be 

 found which will satisfy (3), and therefore no refracted ray 

 can be formed. 



Equation ('2), however, shows that when fjusmi>l } a 

 disturbance travels from the surface AC to a small distance 

 within the upper medium. For when d is very small, the 

 numerical value of the second term to the right of (2) may 

 attain an appreciable value, and as this value is subtracted 

 from that of /Ltsin i in the first term, the value of sin 6 may 

 be reduced to less than unity. Thus when the angle of 

 incidence exceeds its critical value, the secondary wavelets in 

 the rarer medium reinforce each other only in the space 

 lying very close to the surface of separation, and in this 

 space alone is a resultant disturbance produced. 



The existence of a superficial disturbance within the rarer 

 medium when the angle of incidence exceeds its critical value 

 is confirmed by a well-known experiment. The hypotenuse 

 face of a right-angled prism is laid upon the convex surface 

 of a lens, and the point of contact is viewed through one of 

 the remaining faces of the prism by means of light incident 

 through the other remaining face. The point of contact is 

 seen to be surrounded by a black spot, generally encircled 

 with coloured rings. When the eye is so placed that the 

 light reaching it is reflected at an angle exceeding the 

 critical angle, the coloured rings disappear, but the black 

 spot remains. The existence of this black spot proves that 

 light reaches the eye not only from the face of the prism, 

 but also from the surface of the lens ; and as, at thft edge of 

 the black spot, the thickness of the air-film between the 

 prism and the lens amounts to about a quarter wave-length 

 of light, it follows that light must penetrate from the surface 

 of the prism into the air, at least to a distance equal to a 

 quarter wave-length of light, 



Thus far the theory here developed presents no new 

 feature. But the existence of the secondarv wavelets in the 

 rarer medium, even when they do not reinforce each other 

 to produce a refracted wave, entails interesting consequences 

 which have, we believe, heretofore escaped recognition. 

 When the angle of incidence exceeds its critical value, the 

 wavelets originating in the immediate neighbourhood of A 

 (fig. 1) are incapable of arriving in the same phase at any 

 point in the upper medium. Nevertheless it is possible to 



