ON THE THEORY OF OPTICS. 325 



lua'j ^represent the actual focus of converging rays. It was to such an 

 image of the sun that the term focus, meaning a fire place, was first applied. 

 But if the rays tending to this focus be intercepted and made to diverge, the 

 point will then be their virtual focus, since they will never actually arrive 

 at it, being made to diverge as if they proceeded from a new point, which 

 will also be a virtual focus. When the divergence or convergence of rays 

 of light is altered by refraction or reflection at any surface, the foci of the 

 incident and refracted or reflected rays are called conjugate to each other : 

 the ^ew focus is also called the image of the former focus. Thus, in the 

 case already mentioned, where the convergence of the rays to one focus is 

 converted into divergence from another, the two virtual foci are conjugate 

 to each other ; and the original focus of the lens or mirror is conjugate to 

 the place of the sun, or of the luminous object. If the object had been put 

 in the place of its image, the image would then have occupied that of the 

 ohject ; a property which follows from the direct return of every ray of 

 light through the path by which it has arrived, and which may easily be 

 illustrated by experimental confirmation. (Plate XXVII. Fig. 375.) 



Whenever light is reflected by a plane surface, the conjugate foci are at 

 equal distances from it, and in the same perpendicular. Thus, every point 

 of an image in a looking glass is perpendicularly opposite to the correspond- 

 ing point of the object, and is at the same distance behind the looking glass 

 as the point of the object is before it. (Plate XXVII. Fig. 376.) 



The focus into which parallel rays are collected, or from which they are 

 made to diverge, is called the principal focus of a surface or substance. 

 The sun is so distant, that the rays proceeding from any point of his sur- 

 face, affect our senses as if they were perfectly parallel, and the principal 

 focal distance of a surface or substance may often be practically determined 

 by measuring the distance of the image of the sun or of any other remote 

 object, which is formed by it. 



In order that the rays of light, proceeding from or towards any one 

 point, may be made to converge by reflection towards another, the form 

 of the surface must be elliptical, parabolic, or hyperbolic ; there are also 

 curves of still more intricate forms, which possess the same property with 

 respect to refraction. A small portion, however, of any of these curves, 

 differs very little from a circle ; and a spherical surface is almost universally 

 substituted in practice for all of them, except that the mirrors of large 

 reflecting telescopes are sometimes made parabolical. 



The principal focus of a spherical reflecting surface, whether convex or 

 concave, is half way between the surface and its centre. If a luminous 

 point be placed in the centre of a concave mirror, the rays will all return 

 to the same point ; if the point be beyond the centre, the image will be 

 between the centre and the principal focus, its distance from that focus 

 being always inversely as that of the radiant point. Such a focus is never 

 absolutely perfect, for the rays are never collected from, the whole surface 

 of the mirror into the same point, except when both the point and its image 

 are in the centre : but, provided that the surface be only a small portion 

 of that of the whole sphere, the aberration will be too small to be easily 



