414 LECTURE XXXV. 



Thus, if the law of refraction required the sine of the angle of refraction to 

 be twice as great as that of incidence, this condition 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 reflection 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 reflection 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 tw^o 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 

 'mage 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 exa" 

 .niine the general theory of refraction and reflection, at surfaces of different 

 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 

 Ihey 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, may re- 

 present the actual focus of converging rays. It was to such an image of the 



