ON THE THEORY OF OPTICS. ' 413 



density, beginning from the lowest, or a vacuum, we liave airs and gases 

 of different rarities, water, which is the least refractive of allliquids, and 

 •which is still less refractive when frozen into ice: alcohol, oils, glass, and 

 lastly the diamond; but probably some metallic substances are much more 

 refractive than even the diamond. 



The refractive powers of different substances, are usually estimated by a 

 comparison of the. refractions produced at their surfaces in contact with the 

 air, which, in all common experiments, has the same sensible effect as a 

 vacuum or an empty space; the ratio of the angles of refraction and inci- 

 dence, when small, and that of their sines, in all cases, being expressed by 

 the ratio of 1 to a certain number, which is called the index of the refrac- 

 tive density of the medium. Thus, when a ray of light [passes out of air 

 into water, the sines of the angles are in the ratio of 3 to 4, or of 1 to-t, 

 which is, therefore, the index of the refractive density of water. In the 

 same manner, for crown glass, the ratio is that of 2 to 3, and the index 1^; 

 but for flint glass it is somewhat greater, the ratio being nearly that of 5 to 8. 



It may easily be shown that a refractive substance, limited by parallel sur- 

 faces, must transmit a ray of light, after a second refraction at its posterior 

 surface, in a direction parallel to that in which it first passed through the 

 air. It is also found by experiment that such a substance, interposed between 

 any two mediums of difi'erent kinds, produces no alteration in the whole an- 

 gular deviation of a ray passing from one of them into the other. Hence 

 it may be inferred, that the index of refraction at the common surface of any 

 two mediums is the quotient of their respective indices. For instance,, a 

 plate of c rown glass being interposed between water on one side and air on 

 the other, it produces no change in the direction of a ray of light entering 

 the water; and the index of refraction at the common surface of glass and 

 water is |. (Plate XXVI. Fig. 372, 373.) 



There is one remarkable consequence of the general law, by which the angles 

 of incidence and refraction are related, that whenthe angle of incidence exceeds 

 a certain magnitude, the refraction may become impossible; and in this case the 

 ray of light is wholly reflected, in an angle equal to the angle of incidence. 



