OPTICS. 
in the same line produced with the first, at b, perpendicular to it ; and is there- 
wliich shews that the ray which comes from fore reflected back from it in the same 
the second pin, is reflected from the mir- line, b m C. All these reflected rays meet 
ror at the centre of the eye, in the same in the point, m; and in that point the 
amjle in which it fell on the mirror. 2. Let image of the body which emits the parallel 
a ray of lieht, passing through a small hole rays, d a, C h, and e e, will be tormed; 
into a dark room, be reflected from a plane which point is distant froin the mirror 
mirror, at equal distances from the point of equal to half the radius, 6 m C, of its con- 
reflection, the incident, and the reflected cavity. 
ray, will be at the same height from the The rays which proceed from any celes- 
surface. tial object, may be esteemed parallel at the 
Again, if from a centre, C, with the ra- earth ; and, therefore, the images of that 
diiisrc A. the circle, A M P, be described, object will be formed at m, when the 
the arc, A O, will be found equal to the 
arc, O M, therefore the angle of incidence 
is equal to the angle of reflection. The 
same is found to hold in all cases when the 
rays are reflected at a curved surface, whe- 
ther it be convex or concave. 
With regard to plane specula, it is found 
that the image and the object formed by it 
are equally distant from the speculum, at 
opposite siiles: they are also equal, and 
similarly situated. 
When parallel rays, as dfa, C m b, el c, 
(fig. 9) fall upon a concave mirror, A B, 
they will be reflected back from that mir- 
ror, and meet in a point, m, at half the dis- 
tance of the surface of the mirror from, C, 
the centre of its concavity ; for they will 
be reflected at as great an angle from the 
perpendicular, to the surface of the mirror, 
as they fell upon it, with regard to that 
perpendicular, but on the other side 
thereof. Thus, let C be the centre of con- 
cavity of the mirror, A 6 B, and let the 
parallel rays, dfa, Q, mb, and el e, fall 
upon it at the points, a, b and c. Draw the. 
lines, C i «, Cmb, and Che, from the 
centre, C, to these points ; and all these 
lines will be perpendicular to the surface of 
the mirror, because they proceed thereto 
like so many radii from its centre. Make 
the angle, C o h, equal to the angle d a C, 
and draw the line, am h, which will be the 
direction of the ray, dfa, after it is re- 
flected from the point of the mirror : so 
that the angle of incidence, daC, is equal 
to the angle of reflection, C a /» ; the rays 
making equal angles with the perpendicu- 
lar, C i a, on its opposite sides. Draw also 
the perpendicular, C h c, to the point, c, 
where the ray, el c, touches the mirror ; 
and, having made the angle, C c i, equal 
to the angle, C c e, draw the line, c m i, 
which will be the course of the ray, e l c, 
after it is reflected from the mirror. The 
ray, Cmb, passes through the centre of 
concavity of tlie mirror, and falls upon it 
reflecting surface of the concave mirror is 
turned directly towards the object. Hence 
the focus of the parallel rays is not in the 
centre of the mirror’s concavity, but half 
way between the mirror and that centre. 
The rays which proceed from any remote 
terrestrial object, are nearly parallel at the 
mirror ; not strictly so, but come diverg- 
ing to it in separate pencils, or, as it were, 
bundles of rays, from each point of the 
side of the object next the mirror ; there- 
fore they wilt not be converged to a point 
at tlie distance of half the radius of the 
mirror’s concavity from its reflecting sur- 
face, but in separate points at a little 
greater distance from the mirror. And the 
nearer the object is to the mirror, the fur- 
ther these points will be from it ; and an 
inverted image of the object will be formed 
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 mir- 
ror), in all respects like the object, and as 
distinct as the object itself. 
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 object, 
D E, be placed beyond the centre, C, and 
send out a conical pencil of diverging rays 
from its upper extremity, D, to every point 
of the concave surface of the mirror, Ac B. 
But to avoid confusion, we only draw three 
rays of that 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 mir- 
ror. 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, Cc d, equal to the angle, 
D c C, and draw the right line, c d, for the 
course of the reflected ray, Dc; make 
also the angle, C B d, equal to the angle, 
DBG, and draw the right light line, B d. 
