Mr Stevenson's Totalli/ Beflecting Mirror. 149 



II. Determination of the greatest breadth of the Zones con- 

 sistent with the Total Beflexion of all the Incident Light. 

 We have still to ascertain the greatest value of -^ con- 

 sistent with the total reflexion of all the incident light; and 

 in determining this, it is necessary to take into consideration 

 the diameter of the flame, an element which has not entered 

 into the previous calculations. 



Fig. 3. 



Let A B G H, fig. 3, be a section of one of the zones, D L 

 a section of the flame, and D C A the course of a ray pro- 

 ceeding from the edge of the flame to the point A. Produce 

 A C to E, join C F. Draw D F at right angles to C D, and 

 A K a normal to the circle A B. 



Then putting C F=fl? as before, F D=/, and i^^ the index 

 of refraction of the glass for the extreme red rays of the 

 spectrum. 



Sin FCD= ^, but sin FCE= - sin FCD=-^3; and 



a fi, (i a 



CAF=FCE-AFC=FCE nearly, neglecting A F C on 



fi d 



But since the ray F A is reflected in the direction A I per- 

 pendicular to F B^ if A K be a normal at A, 



KAH=iIAF=45°-t- 



4 



andCAK = KAH-CAH 

 4 ii.d 



account of its smallness.* Therefore CAF= sin ■—. 



= 45°- 



* This assumption is perfectly safe ; for its effect is evidently to make the 

 angle of incidence CAR less than it really is, and consequently the resulting 

 value of ^ will be rather too »mall. 



