OPTICS. 



19 



like manner, the rays N C, N D will be 

 reflected in the directions C F, D G. 

 Now the rays A F, B G, by which the 

 point M is seen, enter the eye, F G, as if 

 they C' me from m, as far' behind the 

 mirror as M is before it, and the rays 

 C F, D G enter the eye as if they came 

 from a point, n, as far behind the mirror 

 as X is before it, that is, E m is equal to 

 E M, and H n to H N. Consequently, 

 if \ve join m n it will be of the same 

 length as MN, and have the same posi- 

 tion behind the mirror as the object has 

 before it. If the eye F G is placed in 

 any other position " before the mirror, 

 and if rays are drawn from M and N, 

 which after reflexion enter the eye, it 

 will be found that these, if continued 

 backwauls, will meet at the points m 

 and n, and, consequently, in every posi- 

 tion of the eye, the ima^e will be seen 

 in the same spot, and of the same size 

 at equal distances from the eye. If the 

 object M X is a person looking into the 

 mirror, he will see a perfect image of 

 himself at m n, and hence we have an 

 explanation of the properties of the 

 looking glass. 



If we place an object M N (Jig. 23) 

 Fig. 23. 



between two plane mirrors A C, C B. 

 Inclined to one another, at any angle 

 A C B, several images of the object will 

 be formed, and they will be arranged in 

 the circumference of a circle. This truth 

 may be clearly proved by drawing the 

 image of the object in its proper place 

 behind each mirror, and then consider- 

 ing each successive image as a new ob- 

 ject, and drawing its image. By doing 

 this, it will become evident, that the 

 image of M N in the mirror A C is m n, 

 while its image in B C is M' X'. In like 

 manner the image of the image m n in 

 B C will be m' n\ while the ima^e of 

 the image M' X' in A C will be M" X". It 

 will be found also that in 1 ' n" is the image 

 both of M" X" in the mirror B C, and of 

 m' n' in the mirror A C, so that it con- 

 sists in reality of two images which will 



exactly cover one another, if A C B is 

 60 or the 6th part of a circle, as it is in 

 the figure ; but if it is ever so little less 

 or more, the image m" n" will be seen 

 double. This is the principle of the 

 kaleidoscope *, so far as the multiplica- 

 tion of the images and their general ar- 

 rangement is concerned ; but it has no- 

 thing to do with the principle of sym- 

 metry which is essential to the kaleido- 

 scope. The above truth is independent 

 of the position of the object and the eye, 

 but the kaleidoscope requires that the 

 object and the eye have certain posi- 

 tions, without which it cannot produce 

 symmetrical and beautiful forms. 



Formation of images by convex mir- 

 rors. Let R S (Jig. 24.) be a convex 



Fig. 24. 



mirror whose centre is O, and M N any 

 object placed before it, then upon the 

 same principles which have been ex- 

 plained for a plane mirror, it will be 

 found that an image of it will be formed 

 at m n, the points m, n being ascertained 

 by continuing back the reflected rays 

 A F, B G, till they meet at m, and C H, 

 D I, till they meet at n. By joining the 

 points M, m and X, n, and continuing 

 the lines till they meet, it will be found 

 that they meet at O, the centre of the 

 mirror, whatever be the distance or the 

 position of the object M N. The image 

 m n is always less than the object ; and 

 as it must always be contained between 

 lines M O, and N O, which meet at O, 

 its length m n will be to that of the ob- 

 ject MX as O n is to O N. When M N 

 approaches to the mirror, m n will also 

 approach to it, and when M N touches 

 the mirror, m n will also touch it, and 



* From two Greek words, signifying; beautiful 

 forms. 



C 2 



