2f) 3 
makes with the same perpendicular on the 
other side. 
A ray oi light failing perpendicularly on a 
plane surface, is reflected back exactly in the 
same direction" in which it came to the re- 
flecting surface: iavs falling obliquely ob- 
serv'e the general law of reflection, and their 
angle of reflection is exactly equal to the 
angle of incidence. In [’late I. Optics, tig. 1., 
Jc is a ray of light falling perpendicularly on 
the plane surface ab, and it is reflected back 
exactly in the same direction; ec is a ray 
failing obliquely on the surface at c, and it is 
reflected in tiie direction cd, making the 
angle ol reflection cd P exactly equal to the 
angle ol incidence tvP, as may be seen by 
inspection of the figure. 
Parallel rays falling obliquely on a plane 
reflecting surface are reflected parallel, con- 
verging rays are reflected with the same de- 
gree of convergence, and diverging rays 
equally diverging. In other words, plane 
surfaces or mirrors make no change in the 
previous disposition of the rays of light. 
A mirror is a body, the surface of which is 
polished to such a degree as to reflect most 
copiously the rays of light. Figs. 1, 2, 3, 
are plane mirrors: in fig. 2. the rays db and 
cu, which are parallel, after having reached 
the surface ah are reflected, the one towards 
It and the other towards k, and in both in- 
stances the angle of reflection is evidently 
equal to the angle of incidence. 
'\ lie rays db and ca (fig. 3.) are conver- 
gent, and -without the interposition of the 
mirror would unite in the point E; but being 
reflected, they unite in the opposite point F: 
the angle of reflection with respect to each 
being still equal to the angle of incidence, as 
may be seen by drawing perpendiculars to 
the points a and b. 
T he rays db and ca (fig. 4.) are on the 
contrary divergent, and alter reflection to- 
wards h and k, preserve exactly the same 
distance from each other as they would have 
bad if they had proceeded without interrup- 
tion towards F and E, the angle of reflection 
being with respect to each ray still exactly 
equal to the angle of incidence. 
Elms it is that plane surfaces reflect the 
rays of light ; but the effects are materially 
different when the surfaces are convex or 
concave, though the same law still obtains 
with respect to these. From a convex sur- 
face, parallel rays, when reflected, are made 
to diverge ; convergent rays are reflected 
less convergent, or are even made to diverge 
in proportion to the curvature of the surface 
compured- u ith their degree of convergence ; 
and divergent rays are rendered more diver- 
gent. Thus it is the nature of convex sur- 
faces to scatter or disperse the rays of light, 
and in every instance to impede their con- 
vergence. From a concave surface, on the 
contrary, parallel rays when reflected are 
made to converge ; converging rays are ren- 
dered more convergent ; and diverging rays 
are made less divergent, or even in certain 
cases may be made to converge. 
To understand this part of the subject, it 
is necessary to be aware, that all curvilinear 
surfaces are composed of right lines infi- 
nitely short, or points; and the reader will 
recollect, that only those rays which fall per- 
pendicularly on a reflecting surface are re- 
flected back in the same direction. All curves 
are arches or segments of circles * If there- 
OITICS. 
fore any curvilinear or spherical surface is 
presented to a number of parallel ravs, it is 
evident that only that ray which strikes the 
spherical surface in such a direction that it 
would proceed in a right line to the centre of 
that circle, of which the reflecting surface is 
an arch or segment, c an be said to fall per- 
pendicularly upon it, of which the reader 
may convince himself by drawing a straight 
line with a ruler at any point of a given circle 
or curve. All the rest of the parallel rays, 
therefore, falling on the spherical surface, 
will fall obliquely upon it, and will conse- 
quently be subject to the general law of re- 
flection, and the angle of their reflection will 
be equal to the angle of their incidence. 
Perhaps the subject will be rendered still 
plainer, if, pursuing the idea thrown out in 
the preceding paragraph, that all curves are 
formed of a number of straight lines infinitely 
short, and inclining to each other like the 
stones in the arch of a bridge, we present to 
the reader the figures 5, 6, 7; which may be 
imagined so many mirrors bent or inclined in 
the form which is represented in the plate, 
i he rays ah and cd (fig. 5.), which are paral- 
lel, are from their different points of inci- 
dence rendered divergent in h and e ; the 
angle of reflection with respect to each being 
equal to the angle of incidence. 
fn tig. 6. the rays ab and cd are conver- 
gent, and would, without the interposition of 
the reflecting surface bd, unite in m; but ac- 
cording to the same principle, they now proceed 
to unite in /, which is more distant from the 
reflecting surface than the point m ; and it is 
evident, that if the curvature of the two 
branches of the reflecting surface b and d 
was greater, they might be reflected parallel, 
or even divergent. In the same manner, as 
in fig. 7., the rays ab and ccl, which, without 
the interposition of the convex surface bd, 
would diverge but very little at m, become 
after reflection much more divergent at /; 
and the angles of reflection will be found in 
all these cases exactly equal to the angles of 
incidence, if measured from the reflecting 
surface produced or lengthened, as at fg and 
Let now fig. S represent a concave mirror 
formed upon the same principles as those 
which we have been examining of the convex 
kind. T lie rays ab, cd , which were parallel 
before reflection, and which make their angles 
of reflection equal to their angles of incidence 
(measured for convenience in this figure from 
the reflecting surface produced), become evi- 
dently convergent at the point /; upon the 
same principles in fig. 9. the converging rays 
ab and cd, which would not have united be- 
fore they reached the point m, are now after 
reflection united at /, which is much nearer 
the reflecting surface. In fine, the divergent 
rays ab and cd in fig. 10., which would have 
become more divergent at m, had they not 
been intercepted by the reflecting surface, 
become convergent after reflection, and are 
found actually to unite at n. 
Mirrors are formed either of metal, dr of 
glass plated behind w:th an amalgam of mer- 
cury and tin. I lie latter are most in common 
use ; but they are improper for optical instru- 
ments, such as telescopes, & c. because they 
commonly present two images of the same 
object, the one vivid and thru other faint, as 
may be perceived by placing the flame of a 
wax-taper before a common looking-glass. 
1 he reason of this double image is, (hat a part 
of the rays are immediately reflected from 
the anterior surface of the glass, and thus form 
the faint image ; while the greatest part of the 
rays penetrating the glass are reflected by 
the amalgam, and form the vivid image. 
From the principles laid down, most of (lie 
phenomena ot reflection may be explained. In 
plane mirrors, the image appears of its natu- 
ral size, and at the same distance behind the 
glass as the object is before it. To under- 
stand perfectly the reason of this, it will be 
necessary 7 to advert to the subject of vision, 
as formerly explained. It will be remember- 
ed, that by the spherical form of the eye, and 
particularly by means of the ch ry stall in e hu- 
mour which is placed in the middle oi it, the 
rays ot light are converged ; and those from 
the extreme points of the object cross each 
oilier, so as to form an inverted image on 
that part of the optic nerve which is called 
the retina. The apparent magnitude of ob- 
| jects will consequently depend upon the size 
ot the inverted image, or, in other words 
upon the angle which the rays of light form 
by entering the eye from the extremities of 
any object. 
As therefore the angle of reflection is always 
equal to the angle of incidence, it will be evi- 
dent on the inspection of fig. n. that the 
converging rays Km, L n, proceeding from 
the extremities of the object KL, and falling 
on the mirror ab, are reflected to the eye at 
c v ith the same degree of convergence, and 
consequently will cause the image kl to be 
seen under an angle equal to that under 
winch the object itself would have been seen 
from the point i without the interposition of 
the mirror. The image appears also at a 
distance behind the mirror equal to that at 
which the object stands before it. .For it 
must be remembered, that objects*are ren- 
dered visible to our eyes not by a single ray 
proceeding from every point of an object, 
but that in fact pencils or aggregates of di- 
vergent rays proceed from every point of all 
visible objects, which rays are again, bv the 
mechanism ot the eye, converged to as many 
points on all those parts of the retina where 
the image is depicted. The point from which 
the rays diverge is called the focus of diver- 
gent lays, and the point behind a reflecting 
surface from which they appear to diverge 
is called the virtual focus. As therefore the 
angle of reflection is exactly equal to the 
angle of incidence, it is evident that the vir- 
tual focus will beat the same distance behind 
the mirror as the real focus is at before it. 
I bus, in fig. 12., the diverging rays ch wili 
alter reflection appear to diverge from the 
point g which is behind the mirror ab, and' 
that point for the reasons assigned (viz. no 
alteiation being made in the disposition of 
the rays but only in the direction) will be at 
an equal distance behind the mirror with the 
luminous point c before it. 
As every part of the image appears at a 
distance behind the mirror equal to that at 
which the object stands before it, and as the 
object KL (fig. 11.) is inclined or out of the 
vertical position, the image kl appears also 
inclined. Hence it is evident, that to exhi- 
bit objects as they are without any decree of 
distortion, looking-glasses, should be alway s 
hung m a vertical position, that is, at rfolit 
angles with the floor of the apartment. & 
It is clear, however, from what has-pre- 
