Optics. 
to the glass, the picture, a b c, will be 
removed to a greater distance ; for then, 
more rays flowing from every single point, 
will fall more diverging upon the glass ; 
and therefore cannot be so soSn collected 
into the corresponding points behind it. 
Consequently, if the distance of tlie object, 
ABC (fig. 7), be equal to the distance. 
each pencil will be so refracted by passing 
through the glass, that they will go out of 
it parallel to each other; as d I, eH, /h, 
from the point C ; d G, e K, / D, from 
the point B ; and d K, e E, /L, from the 
point A; and therefore there will be no 
picture formed behind the glass. 
If the focal distance of the glass, and 
the distance of the object from the glass, 
be known, the distance of the picture 
from the glass may be found by this rule, 
viz. multiply the distance of the focus by 
the distance of the object, and divide the 
product by their difference ; the quotient 
will be the distance of the picture. 
The picture will be as much bigger, or 
less, than the object, as its distance from 
the glass is greater or less than the distance 
of the object ; for (fig. 6) as B e is to e b, 
so is A C to c a ; so tliat if A B C be the 
object, c b a will be the picture ; or if 
eh a be the object, ABC will be the 
picture. 
If rays converge before they enter a 
convex tens, they are collected at a point 
nearer to the lens than the focus of pa- 
rallel rays. If they diverge before they 
enter the lens, they are then collected in a 
point beyond the focus of parallel rays; 
unless they proceed from a point on the 
other side at the same distance with the 
focus of parallel rays ; in which case they 
are rendered parallel. 
If they proceed from a point nearer than 
that, they diverge afterwards, but in a 
less degree than before they entered the 
lens. 
When parallel rays, as abode (fig. 8), 
pass through a concave lens, as A B, they 
will diverge after passing through the glass, 
as if they had come from a radiant point, 
C, in the centre of the convexity of the 
glass ; which point is called the “ virtual, 
or imaginary focus.” ' 
Thus, the ray, «, after passing through 
the glass, A B, will go on in the direction, 
kl, as if it had proceeded from the point, 
C, and no glass been in the way. The 
ray, b, will go on in the direction, m n ; 
ttie ray, c, in the direction, o p, &c. The 
ray, C, that falls directly upon the middle 
of the glass, suffers no refraction in passing 
tlirough it, but goes on in the same rec- 
tilinear direction, as if no glass had been 
in the way, 
If the glass had been concave only on 
one side, and the other side quite flat, the 
rays would have diverged, after passing 
through it, as if they had come from a ra- 
diant point at double the distance of C 
from the glass; that is, as if the radiant 
had been at the distance of a whole dia- 
meter of the glass’s convexity. 
It rays come more Converging to such a 
glass, than parallel rays diverge after pass- 
ing through it, they will continue to 
converge after passing through it; but 
will not meet so soon as if no glass had 
been in the way ; and will incline towards 
the same side to wdiich they would have 
diverged, if they had come parallel to the 
glass. 
Of Reflection. When a ray of light falls 
upon any body, it is reflected, so that the 
angle of incidence is equal to the angle of 
reflection; and this is the fundamental fact 
upon which all the properties of mirrors 
depend. This has been attempted to be 
proved upon the, principle of the compo- 
sition and resolution of fbi'ces or motion t 
let the motion of the incident ray be ex- 
pressed by AC (fig. g); then A D will ex- 
press the parallel motion, and A B the per- 
pendicular motion. The perpendicular 
motion after reflection will be equal to that 
before reflection, and therefore may be 
expressed by D C = A D. The parallel 
motion, not being affected by reflection, 
continues uniform, and will be expressed 
by D M = A D ; therefore the course of the 
ray will be C M, and by a well-known pro- 
position in Euclid A C D =: D C M. The 
fact may, however, be proved by experi- 
ment in various ways ; the following me- 
thod will be readily understood. 
Having described a semicircle on a 
smooth board, and from the circumference 
let fall a perpendicular bisecting the dia- 
meter, on each side of the perpendicular 
cut off equal parts of the circumference ; 
draw lines from the points in which those 
equal parts are cut off to the centre ; place 
three pins perpendicular to the board, one 
at each point of section in the circumfer- 
ence, and one at the centre ; and place the 
board perpendicular to a plane mirror. 
Then look along one of the pins in the cir- 
cumference to that in the centre, and the 
other pin in the circumference will appear 
€ B, of the focus of the glass, the rays of 
