INTRODUCTION TO OPTICS. Ixxxiii 



AB, CD, EF, to represent rays falling; on the convex mirror MN: the 



Fig. 12. 



middle ray, you will observe, is perpendicular to the mirror, the others 

 fall on it obliquely. The three rays being- parallel would all be perpendi- 

 cular to a flat mirror ; but no ray can fall perpendicularly on a spherical 

 mirror, which is not directed towards the centre of the sphere, just as a 

 weight falls perpendicularly to the earth when gravity attracts it towards 

 the centre. In order, therefore, that rays may fall perpendicularly to the 

 mirror at B and F, the rays must be in the direction of the dotted lines, 

 which meet at the centre, O, of the sphere, of which. the mirror forms 

 a portion. 



Now let us observe in what direction the three rays AB, CD, EF, 

 will be reflected. The middle ray falling perpendicularly on the mirror, 

 will be reflected in the same line ; the two others falling obliquely, will 

 be reflected obliquely to G and H, for the dotted lines are perpendiculars, 

 which divide their angles of incidence and reflection, or they will proceed 

 as if they came from the point L ; and since we see objects in the direction 

 of the reflected ray, we shall see an image, answering to that which would 

 be produced by a body placed at L, which is the point at which the 

 reflected rays, if continued through the mirror, would unite and form 

 an image. This point is equally distant from the surface and centre 

 of the sphere, and is called the imaginary focus of the mirror. A focus 

 is a point at which converging rays unite; in this case called an imaginary 

 focus, because the rays only appear to unite there, or rather proceed 

 after reflection in the same direction as if they came from behind the mirror, 

 from that point : for they do not pass through the mirror, since they are 

 reflected by it. 



If the rays diverge before they fall on the mirror, they will diverge still 

 more after reflection j but in this case also they will diverge as if they 

 proceeded from a point within the mirror, which is the focus of those rays. 

 The rays, therefore, which really proceed from a point in front of the 

 mirror, will appear to proceed from a point within it, at which they would 

 unite, and form an image. This point within the mirror, like the 

 imaginary focus of parallel rays, is always a point in the line joining the 

 centre of the sphere, with the point without the mirror, from which the 

 rays really proceed. 



If, instead of supposing a single luminous point, we imagine a body of 

 some magnitude placed before the mirror, the rays of light which proceed 



G 



