Ixxxiv 



INTRODUCTION TO OPTICS. 



Fig. 13. 



A 



O 



from each point of it will be reflected "exactly in the same manner as if 

 that was a single luminous point ; and an image of that point therefore 

 will be formed as before, in the line joining that point to the centre of the 

 sphere. An image being thus formed of each point in the object, there 

 will be an image of the whole object, formed by the collection of these 

 images of its different parts. 



This Image will necessarily' be 

 smaller than the object itself. If 

 AB be an object placed before 

 the convex mirror, X Y, and lines 

 be drawn from its extreme points, 

 A B to O, the centre of the sphere 

 of which the mirror forms part, 

 the image of the point A will be at 

 , a point in the line A O ; that of 

 B at 6, a point in the line B O ; 



and of course the image of every intermediate point somewhere between 

 a and b. Or, in other words, the rays which really proceed from A are 

 seen after reflection as if they proceeded from a ; those from B as if they 

 proceeded from b ; and all others as if from some point between them. 

 The lines A O, B O, converge to a point at O ; and the points a, b, which 

 are nearer to O than A, B are, are necessarily nearer together than A, B. 

 The space, therefore, from which the rays after reflection appear to pro- 

 ceed is less than that occupied by the body itself, as the image is smaller 

 than the object. 



A concave mirror is formed of a 

 portion of the internal surface of a 

 hollow sphere, and its peculiar pro- 

 perty is to make the rays of light con- 

 verge. If three parallel rays, A B, 

 C D, E F, fall on the concave 



Fig. 14. 



mirror, M N (Jig. 14), the middle 

 ray will be reflected in the same 

 line, being in the direction of the 

 axis of the mirror, and the two 

 others will be reflected obliquely, 

 as they fall obliquely on the mirror. 



The two dotted perpendiculars divide their angles of incidence and reflection; 

 and in order that these angles may be equal, the two oblique rays must be 

 reflected to L, where they will unite with the middle ray. Thus, when any 

 number of parallel rays fall on a concave mirror, they are all reflected to a 

 focus : for in proportion as the rays are more distant from the axis of the 

 mirror, they fall more obliquely upon it, and are more obliquely reflected : 

 in consequence of which they come to a focus in the direction of the axis of 

 the mirror j and this point is not an imaginary focus (as with the convex 

 mirror), but the true focus at which the rays unite. If rays fall convergent 

 on a concave mirror (fig. 15), they are sooner brought to a focus, L, than 

 parallel rays : their focus is therefore nearer to the mirror MN. Divergent 

 rays are brought to a more distant focus than parallel rays, as in fig. 16, 

 where the focus is at L ; but the true focus of mirrors, either convex or 

 concave, is that formed by parallel rays, which is equally distant from the 

 centre and the surface of the sphere, as in fig. 12 and fig. 14. If a 

 metallic concave mirror of polished tin be exposed to the sun, the rays 

 will be collected into a very brilliant focus ; and a piece of paper held 



