324 LECTURE XXXV. 



surfaces, must transmit a ray of light, after a second refraction at its pos-. 

 terior 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 different kinds, produces no alteration in the 

 whole angular 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 sur- 

 face of any two mediums is the quotient of their respective indices. For 

 instance, a plate of crown 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 surfe^e 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 when the angle of inci- 

 dence 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. Thus, if the law of refraction required the sine of 

 the angle of refraction to be twice as great as that of incidence, this con- 

 dition could not take place if the angle of incidence were greater than 30, 

 so that when a ray passing within a dense medium falls very obliquely on 

 its surface, it must be wholly reflected ; and the greater the density of the 

 medium, the more frequently will the light be totally reflected. This re- 

 flection is more perfect than any other ; the diamond owes much of its 

 brilliancy to it : the great refractive density of this substance not only 

 giving a lustre to its anterior surface, but also facilitating the total reflec- 

 tion of such rays as fall obliquely on its posterior surface. If we hold a 

 prism near a window, in a proper position, we may observe that its lower 

 surface appears to be divided into two parts, the one much brighter than 

 the other ; the common partial reflection taking place in one, and the total 

 reflection in the other. The two surfaces are separated by a coloured arch : 

 it is coloured, because the total reflection commences at different angles for 

 the rays of different colours ; and it is curved, because the points, at which 

 the light passing to the eye forms a given angle with the surface, do not lie 

 in a straight line ; and if we throw a light on a wall by a reflection of this 

 kind, we may easily observe, as we turn the prism, the point at which the 

 brightness of the image is very conspicuously increased. (Plate XXVI. 

 Fig. 374.) 



Such are the principal properties which we discover in light. Before we 

 consider their immediate application to optical instruments, we must ex- 

 amine the general theory of refraction and reflection at surfaces of dif- 

 ferent kinds, or the doctrines of dioptrics and catoptrics. 



The rays,, which constitute a pencil of light, are sometimes parallel to 

 each other, sometimes divergent from a point, and sometimes convergent to 

 a point. The intersection of the directions of any two or more rays of light 

 is called their focus ; and the focus is either actual or virtual, accordingly 

 as they either meet in it, or only tend to or from it. Thus, a small luminous 

 object may represent an actual focus of diverging rays, since the light 

 spreads from it in all directions; and the small surface into which the 

 image of such an object, or of the sun, is collected by a lens or mirror, 



