xxxii INTRODUCTION TO OPTICS. 



nation of which the image will be represented. The line D E is equal 

 to D C, or to D A ; and the line A B D therefore, which represents the 

 necessary length of the mirror, is half the line E F, which represents the 

 height of the person. The man could not see the whole of his person in 

 a 7 much smaller mirror; for a ray of light from his feet would fall so 

 obliquely on it, that it would be reflected above his head, so that he could 

 not see it. This is shown by the dotted line {fig- 10). A man cannot 

 see himself in a mirror if he stand to the right or the left of it, because 

 the incident rays falling obliquely on the mirror will be reflected obliquely 

 in the opposite direction, the angles of incidence and of reflection being 

 equal- 



Fig. 11 represents an eye looking at the image of a vase, reflected by a 

 mirror : it must see it in the direction of the ray A B, as that is the ray 

 which brings the image to the eye ; prolong the ray to C, and in that spot 

 will the image appear. You must observe, that in a glass mirror it is not 

 the glass that reflects the rays which form the image, but the mercury 

 behind it. The glass acts chiefly as a transparent case, through which 

 the rays find an easy passage. Could mirrors be made of mercury, they 

 would reflect more perfectly ; but mercury is a fluid. By amalgamating it 

 with tin-foil, it becomes of the consistence of paste, attaches itself to the 

 glass, and forms, in fact, a mercurial mirror, which would be much more 

 perfect without its glass cover, for the purest glass is never completely 

 transparent : some of the rays, therefore, are lost during their passage 

 through it, by being either absorbed, or irregularly reflected. This im- 

 perfection of glass mirrors has introduced the use of metallic mirrors, for 

 optical purposes. All opaque bodies would be mirrors, were their surfaces 

 sufficiently smooth; but the surface of bodies in general is so rough and 

 uneven, that their reflection is extremely irregular, which prevents the 

 rays from forming an image on the retina. You may easily conceive the 

 variety of directions in which rays would be reflected by a nutmeg-grater, 

 on account of the inequality of its surface, and the number of holes with 

 which it is pierced. Now all solid bodies resemble the nutmeg-grater in 

 these respects, more or less ; and it is only those which are susceptible of 

 receiving a polish, that can be made to reflect the rays with regularity. 

 As hard bodies are. of the closest texture, the least porous, and capable of 

 taking the highest polish, they make the best mirrors: none, therefore, 

 are so well calculated for this purpose as metals. 



There are three kinds of mirrors used in optics : the plane or flat, 

 which are the common mirrors we have just mentioned, convex mirrors, 

 and concave mirrors. The reflection of the two latter is very different 

 from that of the former. 



The plane mirror, we have seen, does not alter the direction of the 

 reflected rays, and forms an image behind the glass exactly similar to the 

 object before it: for it forms an image of each point of the object at the 

 same distance behind the mirror, that the point is before it ; and these 

 images of the different points together make up one image of the whole 

 object. A convex mirror has the peculiar property of making the reflected 

 rays diverge, by which means it diminishes the image ; and a concave mirror 

 makes the rays converge, and, under certain circumstances, magnifies the 

 image. Let us begin by examining the reflection of a convex mirror. This 

 is formed of a portion of the exterior surface of a sphere. When several 

 parallel rays fall upon it, that ray only which, if prolonged, would pass 

 through the centre, or axis of the mirror, is perpendicular to it. In order 

 to avoid confusion, we have, in fig. 12, drawn only three parallel lines, 



