OPTICS. 



The rays which proceed from any ce- 

 lestial object, may be esteemed parallel 

 at the earth ; and, therefore, the images 

 of that object will be formed at m, when 

 the reflecting surface of the concave 

 mirror is turned directly towards the ob- 

 ject. Hence the focus of the parallel 

 rays is not in the centre of the mirror's 

 concavity, but halfway between the mir- 

 ror, and that centre. The rays which pro- 

 ceed from any remote terrestrial object 

 are nearly parallel at the mirror ; not 

 strictly so, but come diverging to it in 

 separate pencils, OP, as it were, bundles 

 of rays, from each point of the side of 

 the object next the mirror ; therefore 

 they will not be converged to a point at 

 the distance of half the radius of the mir- 

 ror's concavity from its reflecting surface, 

 but in separate points at a little greater 

 distance from the mirror. And the near- 

 er the object is to the mirror, the further 

 these points will be from it ; and an in- 

 verted image of the object will be form- 

 ed in them, which will seem to hang 

 pendent in the air ; and will be seen by 

 an eye placed beyond it (with regard 

 to the mirror), in all respects like the 

 object, and as distinct as the object it- 

 self. 



Let A c B (fig. 10), be the reflecting 

 surface of a mirror, whose centre of con- 

 cavity is at C ; and let the upright ob- 

 ject, D E, be placed beyond the centre, 



C, and send out a conical pencil of di- 

 verging rays from its upper extremity, 



D, to every point of the concave sur- 

 face of the mirror, A c B. But, to avoid 

 confusion, we only draw three rays of 

 tliat pencil ; as D A, D c, D B. From the 

 centre of concavity, C, draw the three 

 right lines, C A, C c, C B, touching the 

 mirror in the same points where the 

 aforesaid touch it, and all these lines will 

 be perpendicular to the surface of the 

 mirror. Make the angle, C A d equal to 

 the angle, D A C, and draw the right 

 line A d, for the course of the reflected 

 ray, D A : make the angle, C c cl, equal 

 to the angle, D c C, and draw the right 

 line, c d, for the course of the reflected 

 ray, D c ; make also the angle, C B d, 

 equal to the angle, D B C, and draw 

 the right light line, B d, for the course 

 of the reflected ray, D B. All these re- 

 flected rays will meet in point d, where 

 they will form the extremity, d, of the in- 

 verted image, e d t similar to the extremity, 

 B, of the upright object, D E. If the 

 pencil of rays, E /,.-, E h, be also con- 

 tinued to the mirror, and their angles of 

 reflection from it be made equal to their 



angles of incidence upon it, as in the for- 

 mer pencil from D, they will meet at 

 the point, e, by reflection, and form the 

 extremity, e, of the image, e d, similar to 

 the extremity, E, of the object, D E. As 

 each intermediate point of the object be- 

 tween D and E, sends out a pencil of rays 

 in like manner to every part of the mir- 

 ror, the rays of each pencil will be re- 

 flected back from it, and meet in all 

 the intermediate points between the ex- 

 tremities, e and d, of the image ; and so 

 the whole image will be formed, not at 

 *", half the distance of the mirror from 

 its centre of concavity, C ; but at a 

 greater distance between i and the ob- 

 ject, D E ; and the image will be invert- 

 ed with respect to the object. This be- 

 ing well understood, the reader will easily 

 see how the image is formed by the 

 large concave mirror of the reflecting 

 telescope, when he comes to the de- 

 scription of that instrument. See TELE- 

 SCOPE. 



When the object is more remote from 

 the mirror than its centre of concavity, 

 C, the image will be less than the object, 

 and between the object and the mirror ; 

 when the object is nearer than the centre 

 of concavity, the image will be more re- 

 mote, and bigger than the object : thus, 

 if D E be the object, e c? will be its image ; 

 for as the object recedes from the mirror, 

 the image approaches nearer to it ; and 

 as the object approaches nearer to the 

 mirror, the image recedes further from 

 it, on account of the lesser or greater 

 divergency of the pencils of rays which 

 proceed from the object; for the less 

 they diverge, the sooner they are con- 

 verged to points by reflection ; and the 

 more they diverge, the further they must 

 be reflected before they meet. If the ra- 

 dius of the mirror's concavity and the 

 distance of the object of it be known, the 

 distance of the image from the mirror is 

 found by this rule : Divide the product of 

 the distance and radius by double the dis- 

 tance made less by the* radius, and the 

 quotient is the distance required. If the 

 object be in the centre of the mirror's 

 concavity, the image and object will be 

 coincident, and equal in bulk. 



If a man place himself directly before a 

 large concave mirror, but further from it 

 than its centre of concavity, he will see 

 an inverted image of himself in the air, 

 between him and the mirror, of a less size 

 than himself. And if he hold out his 

 hand towards the mirror, the hand of the 

 . image will come out towards his hand, and 

 coincide with it, of an equal bulk, when 



