HA RD WICKE'S SCIENCE- G OSSIP. 



THE TWO MIRRORS. 

 By W. J. N. 

 No. V. 



IN the preceding articles, the incident pencil has 

 been supposed to consist of parallel rays. Such 

 are the rays of a beam of daylight, naturally and in 

 perfection, since they emanate from a source which is 

 infinitely distant. , Such too, in good degree, are the 

 rays of the artificial pencil which we have learned to 

 derive from the diverging rays of a minute lamp- 

 flame, by placing the bull's-eye before the lamp at 

 the distance of its principal focus. We have not had 

 occasion to study the relations of conjugate foci, for 

 in connection with a parallel pencil no conjugate 

 focus has existed. No reason has, therefore, appeared 

 for keeping the lamp at some exact point of 

 distance, in order to preserve integrity of focus in the 

 reflected rays. Nor has the brightness of the 

 illumination depended on the nearness of the lamp. 

 It is one of the advantages of a parallel pencil, that 



Fig. 21. 



it retains its illuminating power for long distances ; 

 and reasons have been given why the artificial pencil 

 should become more pure— without being materially 

 less brilliant — as the distance between the lamp and 

 the mirror is reasonably increased. The two points 

 which have principally claimed our attention hitherto, 

 have been — how to render the incident rays of lamp- 

 light truly parallel, and how afterwards to compel 

 them to form certain desired angles with the 

 principal axis of the concave mirror. 



Passing from that part of our subject, we enter 

 upon another, which is somewhat more difficult, 

 the nature and management of a divergent pencil. 



By angles of incidence must now be understood 

 the angles formed with the principal axis of the 

 concave mirror by a single ray of the pencil — 

 namely, its central ray or axis. Their importance, 

 and the method by which their magnitudes are to be 

 determined, will be the same as in the case of the 

 parallel pencil. (See vol. for 1886, pp. 251 and 267.) 



The properties of conjugate foci will come before 

 us in connection with a new relationship found to 

 exist between the lamp, the concave mirror and the 



object ; and the brightness of the illumination, 

 instead of being independent of the distance of the 

 lamp, will be found to depend mainly upon it. 



There are two forms of divergent pencil. Let us 

 call them, the simple and the compound. A simple 

 pencil consists of rays which pass in straight lines 

 from the flame to the mirror. The compound pencil 

 consists of rays whose first lines of direction have 

 been altered by passing them through the bull's-eye 



condenser. The amount of divergence is thus 

 reduced. The bull's-eye, when used for this purpose, 

 is placed at a distance from the lamp slightly less 

 than that which would parallelise the rays ; less, 

 that is, than the distance of its principal focus. The 

 divergence of a pencil may thus be reduced to any 

 desired extent, the object being to crowd upon the 

 mirror a larger number of the constituent rays. 



Fig. 21 represents the section of a simple divergent 

 pencil, lcd, made lengthways through the central 



