228 Angles of Incidence and Refraklhn. [Book III, 



rounded by air. Draw E F M perpendicular to A B, 

 and make G F M fuch an angle, that the fine of 

 HFE fhall be to the fine of M FG as 3 to 2, and the 

 ray H F will in the glafs move in the direction G F. 

 When the ray comes to G it fufFcrs another change in 

 its direction by moving into air, and to find this di- 

 rection, draw I G N perpendicular to C D, and make 

 L G N fuch an angle, that the fine of F G I fhali be 

 to the fine of N'G L as 2 to 3, then the ray will move 

 in the direction G L. Thus the whole progrefs of the 

 ray is found to be in the direction H FG L, and by the 

 fame rule its progrefs through any number of mediums 

 might be found. 



The direction G L (in Fig. 10.) is parallel to the 

 direction H F ; for the angles M F G, F G I, N G K, 

 are equal ; and fince the fine of M F G is to the fine 

 of MFI as the fine of N G K is to the fine of NGL, 

 the angles NGL, MFI, are equal, and confequently 

 the angles NGL, N I O, are equal. There-fore the 

 lines HO, GL, are parallel. 



1 Let FG (Fig. ic.) be a ray in a denfe medium in- 

 cipient on G, and its direction after emergence be G L. 

 The greater the .angle FGI is, the greater will be the 

 angle N'G L. Suppofe N G L to be a right angle, 

 then the fine of FGI is to the radius as the fine of in- 

 cidence to the fine of refraction, and according to the 

 law of refraction for the given medium, the limiting 

 angle of incidence will be found for a ray to emerge. 

 When the angle of incidence is greater than this angle 

 thus found, the incident ray will be reflected buck in 

 die direction abc> as was explained in a -preceding 

 chapter. 



Let rays diverging from a point Q^(Fig. 1 1, 12.) 

 after refraction, move in the medium ABCD. To a 

 pcrfon in this medium they will not appear to have* 



diverged 



