142

OPTICS.

from it whatever; arid that his image must appear just as far behind die glass as he is before it. Thus, the man AB, fief. 33, view-ing himself in the plane mirror CD, which is just half as long ashimself, sees his whole image as at EF, behind the glass, exactlyequal to his own size. For a ray AC proceeding from his eye atA, and falling perpendicularly upon the surface of the glass at C,is reflected oack to his eye, in the same line CA ; and the eye ofhis image wdl appear at E, in the same line produced to E, be-yond the glass. And a ray BD, flowing from his foot, and fallingobliquely on the glass at D, will be reflected as obliquely on theother side of the perpendicular a b D, in the direction DA ; andthe foot of his image will appear at F, in the direction of the re-flected ray AD, produced to F, where it is cut by the right lineBGF, drawn parallel to the right line ACE. Just the same as ifthe glass were taken away, and a real man stood at F, equal insize to the man standing at B : for to his eye at A, the eye of theother man at E would be seen in the direction of the line ACE ;and the foot of the man at F would be seen by the eye A, in thedirection of the line ADF. If the glass be brought near the manAB, as suppose to c b, he will see his image as at CDG : for thereflected ray CA (being perpendicular to the glass) will shew theeye of the image as at C ; and the incident ray B b, being re-flected in the line b A, will shew the foot of his image as at G;the angle of reflection a b A being always equal to the angle of in-cidence B I) a ■■ and so of all the intermediate rays from A to B.Ilence, if the man A B advances towards the glass CD, his imagewill approach towards it: and if he recedes from the glass, hisimage will also recede from it. If the object be placed before acommon looking-glass, and viewed obliquely, three, four, or moreimages of it, wall appear behind the glass. To explain this, letABCD, lig. 54, represent the glass; and let EF be the axis of apencil of rays flowing from E, a point in an object situated there.The rays of this pencil will in part be reflected at F, suppose 'theline FG. What remains will (after refraction at F, which we donot consider here) pass on to II; from whence (on account of thequicksilver which is spread over the second surface of glasses ofthis kind, to prevent any of the rays from being transmitted there)they will be strongly reflected to K, where part of them willemerge and enter an eye at L, By these means one representa-tion of the said point will be formed in the line LK produced,suppose in M ; Again, another pencil, whose axis is EN, first re-flected at N, then at O, and afterwards at B, will form a secondrepresentation of the same point at Q: And thirdly, another pen-cil, whose axis is ER, after reflection at the several points R, S, H,T, V, successively, will exhibit a third representation of the samepoint at X; and so on in infinitum. 1 he same being true ofeach point in the object, the whole will be represented in thelike manner; but the representations will be faint, in proportionto the number of reflections the rays suffer, and the length of theirprogress within the glass. We may add to these another repre-sentation of the same object in the line LO produced, made bysuch of the rays as fall upon O, and are from thence reflected tothe eye at L. This experiment may be tried by placing a candlebefore the glassas at E, and viewing it obliquely, as from L. The ef-fects of concave and convex mirrors have been already explained.

3. Microscopes and Telescopes. For the description of theseinstruments we refer to the articles in their alphabetical order ; weshall here only observe that the advantages arising from the use ofthe microscopes and telescopes depend, in the first- place, upontheir property of magnifying the minute parts of objects, so thatthey canoe thus more distinctly viewed by the eye; and, 2dlyupon their throwing more light into the pupil of the eye thanwhat is done without them. The advantages arising from themagnifying power would be extremely-limited, if they were notalso accompanied by the latter: for if the same quantity of lightis spread over a large portion of surface, it becoins proportionallydiminished in force; and therefore the objects, though magnified',appear proportionably dim. Thus, though any magnifying glassshould enlarge the diameter of tin: object ten times, and con- •sc-quently magnify the surface 100 times, yet if the focaldistance of the glass was above eight inches (provided this waspossible), and its diameter only about the size ot the pupil of theeye, the object would appear 100 times more dim when we lookedthrough the glass, that when we beheld it with our naked eyes;and tins, even on a supposition, tliat the glass transmitted all the

] light which fell upon it, which no glass can do. But if the focaldistance of the glass was only four inches, though its diameter re-mained as before, the inconvenience would be vastly diminished,because the glass could then be placed twice as near tile object asbefore, and consequently would receive four times as many raysas in the former case, and therefore we wouldsee it much brighterthan before. Going on thus, still diminishing the focal distance ofthe glass, and keeping its diameter as large as possible, we shall per-ceive the object more and more magnified, and at the same timevery distinct and bright, it is evident, however, that with re-gard to optical instruments of the microscopic kind, we must sooneror later arrive at a limit which cannot be passed. This limit isformed by the following particulars: 1. The quantity of light lostin passing through the glass. 2. Diminution of the glass itself,by which it receives only a small quantity of rays. 3. The ex-treme shortness of the focal distance of great magnifiers, wherebythe free access of the light to the object which we wish to view isimpeded, and consequently the reflection of the light from it isweakeued.- 4. The aberrations of the rays, occasioned bv theirdifferent refrangibilitv. With regard to telescopes, those of therefracting kind have evidently the advantage of all others, wlu-rethe aperture is equal, and the aberrations of the rays are correctedaccording to Mr. Dollond ’s method; because the image is notonly more perfect, but a much greater quantity of light is trans-mitted, than can be reflected from the best materials hithertoknown. Unluckily, however, the imperfections of the glass set alimit to these telescopes, so that they cannot he made above 3|feet long. On the whole, therefore, the reflecting telescopes arepreferable in this respect, that they may be made of dimensionsgreatly superior; by which means they can both magnify to agreater degree, and at the same time throw much more light intothe eye. With regard to the powers of telescopes, however, theyare all of them exceedingly less than we should be apt to imagine,from the number of limes which they magnify the object. Tims,when we hear of a telescope which magnifies 200 times, we areapt to imagine, that, on looking at any distant object though it,we should perceive it as distinctly as we could with our naked eyeat the 200th part of the distance. But this is by no means thecase; neither is there any theory capable of directing us in thismatter: we must therefore depend entirely on experience. Thebest method of trying the goodness of any telescope is by observ-ing, how much farther off you are able to read with it than youcan with the naked eye. But that all deception may be avoided,it is proper to choose something to be read where the imaginationcannot give any assistance, such as a table of logarithms, or some-thing which consists entirely of figures; and hence the truly use-ful power of the telescope is easily known. In this way Mr. Short’slarge telescope, which magnifies the diameter of objects 1200times, is yet unable to afford sufficient light for reading at morethan 200 times the distance at which we can read with our nakedeye. With regard to the form of reflecting telescopes, it is nowpretty generally agreed, that when the Gregorian ones are wellconstructed, they have the advantage of those of the Newtonianform. One evident advantage is, that with the Gregorian tele-scope an object is perceived by looking directly through it, andconsequently is-found with much greater ease than in the Newto-nian telescope, where we must look into the side. The unavoid-able imperfection of the specula, common to both, also gives theGregorian an advantage over the Newtonian form. Notwith-standing the utmost care and labour of the workmen, it is found im-possible to give the metals either a perfectly spherical or a per-fectly parabolical form. Ilence arises some indistinctness of theimage formed by the great speculum, which is frequently correctedby the little one, provided they are properly matched. Rut if(his is not done, the error will be made much worse; and hencemany of the Gregorian telescopes are far inferior to the Newto-uion ones ; namely when the specula have not been properlyadapted to each other. There is no method by which the work-man can know the specula which will fit one another without atrial ; and therefore there is a necessity for having many speculaready made of each sort, that in fitting up a telescope those may bechosen which best suit eacli other. r l he brightness of any objectseen through a telescope, in comparison with its brightness whenseen by the naked eye, may in all cases be easily found by thefollowing formula: Let n represent the natural distance of a visi-ble