50 Mr. A, AVhitNvell o/i Refraction 



this case a cone of light having a semi-vertical angle equal 

 to the critical angle is refracted, the remainder of the incident 

 light being totally reflected, and the refracted cone having a 



semi-ano-le of ^ . When the radiant-point is inside the 



t 

 cylinder, or \vhen the light is convergent, the curve becomes 

 of the form X., for which a = \. In this case the part of the 

 curve inside the cylinder is the real, and the part outside 

 the false focal line. 



When a = -^ the curve, XI., has parabolic asymptotes, 



the equation of which is 



?j-= —7 "2 .37 — 13. 



When a lies between r and - . the curve has two 



branches and a pair of rectilineal asymptotes. Curve XII. 

 is for a = 'o, and the branch on the right and that part of the 

 branch on the left which is outside the cylinder are the false 

 focal line^ the real focal line being that part of the left 

 branch which is inside the cylinder. The asymptotes may 

 be drawn by means of a circle, the equation of which is 

 obtained as before. 



When a = 0, the axis is the focal line. When a lies 



between and — - or —4, the curve has two branches ; 



the branch on the right and that part of the branch on the 

 left which is outside the cylinder are the real focal line, and 

 that part of the branch on the left which is inside the surface 

 is the false focal line. 



When «=—•!, the curve, XIII., has parabolic asymptotes, 

 the equation of which is 



/=-7-2.r+21, 



this point being the principal focus for rays passing from 

 right to left. 



When a is negative and greater than 4 the curve has only 

 one branch, which lies on the left of the axis, that part outside 

 the surface being the real and that part inside the false focal 

 line. Curve XIY. is for a= —10. 



As the radiant-point moves off to infinity towards the 

 right, the curve approaches and ultimately coincides with the 

 straight line YII. 



The curves shown in figs. 4 and 5 are for light falling on 

 the convex surface of the cvlinder, but bv reversing them 



