224 On a Simple Property of a Refracted Ray. 



If PT be the tangent at P to the circle circumscribing 

 the triangle APB, then the angle TPN, between this 

 tangent and the normal produced, is equal to <f>-\-yjr' =7, 

 since the angle APT between this tangent and the chord 



AP is equal to the angle at B in the opposite segment 

 of the circle, and the angle APN is 0. Without actually 

 drawing the circle APB, the direction of the tangent can 

 usually be judged by inspection. If now the transversal 

 rotate about C, while the rays remain fixed, the tangent 

 will rotate about P at the same rate, but in the opposite 

 direction, the angle swept through in either case being 

 A\jr = increment of ijr = increment of t \fr'. When A-v/r attains 

 the value it — 7, the tangent to the circle coincides with the 

 normal P( 1 to the refracting surface, and if CB'A' be 

 the corresponding position of the transversal, then 



zBCB' = 7T- 7 , z.PB'C = <k z.PA'C = f, 



yLt, fi' being the refractive indices, and r the radius of 

 eurvature. 





