' OPT 
tlie linear aperture and power, and inverfely as the fquare 
of ttie focal length of the reflector, or refraftor. 
Cor. 2. If the radii of the l'urfaces of a concave reflec¬ 
tor, and a double convex lens of glafs, be equal, as well 
as their apertures and powers, iince the focal length of 
the refledtor the focal length of the lens :: i : 2, the 
denfity of rays in the image formed by the refiedtor : the 
denfity in the image formed by the lens :: 4 : 1. 
Cor. 3. The focal length of a glafs fphere is three times 
as great as the focal length of a refledlor of the fame ra¬ 
dius ; therefore, on the former fuppofition, The denlity 
of rays in the image formed by the refledlor : the denfity 
in the image by the fphere :: 9 : 1. 
Cor. 4. If the rays which tend to form the fun’s image 
be received by a double convex lens, another image, nearer 
to the lens, and confequently lefs than the former, will 
be produced. Hence it appears, that independent of the 
rays loll in their paflage through the lens thus employed, 
the burning power of a refiedtor or refraftor may be in- 
creafed. 
Prop. IX. An objedl may be feen diftindtly through a 
convex lens. 
Let AE, fig. 27, be a convex lens, (either double-con¬ 
vex, plane-convex, or menifcus;) E its centre; PQ an 
objedt placed in its principal focus. Then, the rays which 
diverge from any point P will be refradled parallel to each 
other, and to PE; and therefore, they will be proper for 
vifion to common eyes. In the fame manner, the rays 
diverging from any other point will be refradled parallel 
to each other, and the whole objedl will be feen diftindtly. 
If the eye require diverging rays, the object mult be 
placed between the lens and its principal focus; for then, 
the rays which diverge from P, a point between the prin¬ 
cipal focus and the glafs, will, after refradtion, diverge ; 
and therefore be proper for diitindt vifion in this cafe. If 
the eye require converging rays, the objedt muft be placed 
beyond the principal focus; for then, the rays in each 
pencil will, after refradtion, converge. 
Paor. X. When an objedt is placed in the principal 
focus of a convex lens through which it is viewed, it 
appears eredt. ' . 
For, if AO, in the preceding figure, be drawn parallel 
to PE, the rays which diverge from P, and are received 
by the eye, enter the pupil in the diredtion AO ; and the 
rays which diverge from Q enter the pupil in the direc¬ 
tion EO. Thus, the rays which flow from the extreme 
points P, Q, of the objedl, crol's each other at O, and 
therefore the pidlure upon the retina is inverted; or, the 
objedt appears eredh 
Cor. In the fame manner, if the objedt be near to the 
principal focus, and the eye not very diflailt from the 
glafs, the image upon the retina will be inverted ; and, 
confequently, the objedt will appear erect. 
THEORY of REFLECTION. Plate V. 
When a my of light falls upon any body, however 
tranfparent, the whole of it never pafles through the 
body, but fome part is always reflected from it; and it is 
by this reflected light that all bodies, which have no light 
of their own, become vifible to us. Of that part of the 
ray which enters, another part is alfo refledted from the 
fecoud furface, or that which is farthell from the luminous 
body. When this part arrives again at the firft furface, 
part of it is refledted back from that furface; and thus it 
continues to be refledted between the two furfaces, and to 
pafs backwards and forwards within the fubftance of the 
medium, till fome part is totally extinguilhed and loft. 
Befides this inconfiderable quantity, however, which is 
loft in this manner, the fecond furface often refledts much 
more than the firft; fo that, in certain politions, fcarcely 
any rays will pafs through both fides of the medium. A 
very confiderable quantity is alfo unaccountably loft at 
each reflecting furface 3 fo that no body, however trani- 
I C S. 575 
parent, can tranfmit all the rays which fall upon it; nei¬ 
ther, though it be ever la well fitted for reflection, will it 
refledt them all. 
The fundamental law of the refledlion of light, is, that 
the angle of refledlion is always equal to the angle of inci¬ 
dence. This is found by experiment to be the cafe, and 
befides may be demonftrated mathematically from the 
laws of impulfe in bodies perfectly elaftic. The axiom 
therefore holds good in every cafe of reflection, whether it 
be from plane or fpherical furfaces; and hence the feven 
following Propofitions, relating to the refledlion of light 
from plane and fpherical furfaces, may be deduced. 
I. Rays of light refledted from a plane furface have the 
fame degree of inclination to one another that their refpeclive 
incident ones have. —For, the angle of refledlion of each 
ray being equal to that of its refpeclive incident one, it is 
evident, that each refledted ray will have the fame degree 
of inclination to that portion of the furface from Which 
it is refledted that its incident one has; but it is here 
fuppofed, that all thofe portions of furface from which the- 
rays are refletled are fituated in the fame plane; confe¬ 
quently, the refledted rays will have the fame degree of 
inclination to each other that their incident ones have, 
from whatever part of the furface they are refledted. 
II. Parallel rays refletled from a concave furface are ren¬ 
dered converging. —To illuftrate this, let AF, CD, EB,. 
(fig. 1.) reprefent three parallel rays falling upon the con¬ 
cave furface FB, whole centre is C. To the points F 
and B draw the lines CF, CB ; thefe, being drawn from 
the centre, will be perpendicular to the furface at thofe 
points. The incident ray CD, alfo palling through the 
centre, will be perpendicular to the furface, and there¬ 
fore will return after reflection in the fame line; but the 
oblique rays AF and EB will be refledted into the lines 
FM and BM, fituated on the contrary fide of their re- 
fpedlive perpendiculars CF and CB. They will there¬ 
fore proceed converging after refledlion towards fome 
point, as M, in the line CD. 
III. Converging rays falling on the concave furface, are 
made to converge more. —For, every thing remaining as 
above, let GF, HB, be the incident rays. Now, becaufe 
thefe rays have greater angles of incidence than the pa¬ 
rallel ones AF and EB in the foregoing cafe, their angles 
of refledlion will alfo be larger than thofe of the others; 
they will therefore converge after refledlion, fuppofe in 
the lines FN and BN, having their point of concourfe N 
farther from the point C than M,that to which the parallel 
rays AF and EB converged in the foregoing cafe; and 
their precife degree of convergency will be greater than 
that wherein they converged before refledlion. 
IV. Diverging rays falling upon a concave furface, are, 
after rcfleEtion, parallel, diverging, or converging.—It' they 
diverge from the focus of parallel rays, they then become 
parallel; if from a point nearer to the furface than that, 
they will diverge, but in a lefs degree than before reflec¬ 
tion ; if from a point between that and the centre, they 
will converge after refledlion to fome point on the con¬ 
trary fide of the centre, but fituated farther from it than 
the radiant point. If the incident rays diverge from a 
point beyond the centre, the reflected ones will converge 
to one on the other lide of it, but nearer to it than the ra¬ 
diant point; and, if they diverge from the centre, they 
will be refledted thither again. 
r. Let them diverge in the lines MF, MB, proceeding 
from the radiant point M, the focus of parallel rays ; then, 
as the parallel rays AF and EB were reflected into the 
lines FM and BM (by Prop. II.) thefe rays will now, on 
the contrary, be reflected into them. 
2. Let them diverge from N, a point nearer to the fur¬ 
face than the focus of parallel rays; they will then be re 
fledled into the diverging lines FG and BH, which the 
incident rays GF and HB, deferibed, that were fhown to 
be refledted into them in the foregoing Propoiition ; but 
the degree of their divergency will be lefs than their di¬ 
vergency before refledlion. 
S. Let 
