302 
Converging ray 5 , if their ppiot of -eonver- ! 
gt'i’.ce is precis.?!;, at C, the centre of the con- 
cavity cD/, will n >t suffer any refraction, be- 
cause they are perpendiculars, as already ex- 
plained, therefore have no obliquity of inci- 
dence. If, on the other hand, the rays tend 
to a point, such as a, nearer to the surface 
than the centre of the concavity C, then they 
are rendered more convergent ; for the rays 
r;c, ri, which naturally tend to that point, are 
refracted from the perpendiculars Co, Ci, and 
converge at o, nearer the concave surface. 
Lastly, if the converging rays tend to a 
point /, which is beyond the centre C, they 
are rendered less convergent. For the rays 
.sc, ti, which would naturally unite at that 
point, are retracted from the perpendiculars 
CL, Ci, and unite at k, which is more distant 
still. 
Diverging rays in the same circumstances 
are rendered more divergent. For the rays 
Er, E/, diverging from the point E, instead of 
proceeding towards a and x, are refracted 
from the perpendiculars, and are directed 
towards y and z. 
From tiie property which all spherical con- 
vex surfaces have, of rendering parallel rays 
passing out of a rarer medium convergent, 
glasses made in this form are very commonly 
used as burning-glasses; and as the sun’s rays, 
proceeding from so vast a distance, may be 
considered as parallel, the focus of parallel 
rays will of course be their burning-point. 
A lens is a transparent, body of a different 
density from the surrounding medium, and 
terminated by two surfaces, either both sphe- 
rical, or the one plane and the other spheri- 
cal, whether convex or concave. They are 
therefore generally distinguished by their 
forms, and are called plano-convex or plano- 
concave, or double convex or double con- 
cave ; a lens which has one side convex and 
the other concave, is called a meniscus, or 
concave-convex lens. See Plate II. tig. 21. 
It is evident, that in lenses there may be al- 
most an infinite variety with respect to the 
degree of convexity or concavity ; for every 
convex surface is to be considered as the seg- 
ment of a circle, the diameter and radius of 
which may vary to almost an infinite extent. 
Hence, when opticians speak of the length of 
the radius as applied to a lens, as for instance, 
when they say its radius is 3 or G inches, they 
mean that the convex surface of the glass is 
the part of a circle, the radius of which, or 
half the diameter, is 3 or 6 inches. 
The axis of a lens is a straight line drawn 
through the centre of its spherical surface ; 
and as the spherical sides of every lens are 
arches of circles, the axis of the lens would 
pass exactly through the centre of that circle, 
of which its sides are arches or segments. 
From what has been already stated, it is 
obvious that the certain effect of a convex 
lens must be to render parallel rays conver- 
gent; to augment the convergence of conver- 
ging rays ; to diminish in like manner the di- 
vergence of diverging rays, and in some cases 
to make them parallel or even convergent, 
according to the degree of divergence com- 
pared with the convexity of the lens. In 
what is called a double-convex lens, this effect 
will be increased in a duplicate proportion, 
since both surfaces will act in the same man- 
ner upon the rays ; and since it has been 
proved, that parallel or convergent rays have 
OPTICS, 
their convergence equally augmented by be- ’ 
ing incident on the convex surface of a 'dense, 
or the concave surface of a rare medium, 
i hese glasses then must necessarily have l lie ■ 
effect of magnifying glasses, sinc e by the 
convergence of the rays the visual angle is 
rendered more obtuse, and consequently the 
image which is depicted on the retina-must be ‘ 
proportionally larger. 
r I he focus of those rays which come in a 
parallel direction to the" glass, is called the 
focus of parallel rays, or principal focus. In 
a plano-convex glass this focus is at the length 
ol the diameter of that circle, of which the 
convex surface is a segment; and in a dou- ! 
ble-convex lens, or one which is convex on 
both sides, the focus is as the distance of the 
radius, or half the diameter, of the circle of 
which the lens is a segment. This focus 
therefore is easily found upon mathematical 
principles. It may also be found, though not 
with equal exactness, by holding a sheet of 
paper before the glass when exposed to the 
rays of the sun, and observing the distance of 
the paper from the glass when the luminous 
spot on the paper is very small, and when it 
begins to burn ; or when the focal length 
does not exceed three feet, the focus may be 
found by holding the lens at such a distance 
from the wall opposite a window T -sash, that 
the image of the sash may appear distinct 
upon the wall. 
From this property in convex lenses, of 
rendering all rays in some degree convergent 
which fall upon their surfaces, it is evident 
that in all such cases there must be a point, 
which in general is at the focus, where pen- 
cils of rays proceeding from the extreme 
point of any object must first unite and then 
cross each other ; and consequently an in- 
verted image of the object will be exhibited 
at any distance beyond that point. This may 
be elucidated by a very easy experiment, 
viz. by holding a common reading or magni- 
fying glass between a candle and a sheet of 
paper suspended on the wall, at a proper dis- 
tance, when the image of the candle will ap- 
pear on the paper inverted: and the reason 
of this is extremely clear ; for it is evident 
that the upper pencils after refraction, are 
those which proceeded from the under part 
ot the luminous body, and the under rays 
are those which come from its top. The po- 
sition is therefore only inverted, and the 
image remains unimpaired. 
1 rom the same property, convex lenses 
will cause many rays to enter the eye which 
would otherwise have been scattered or dis- 
persed, and therefore objects seen through 
them appear clearer and more splendid than 
when viewed by the naked eye. If, how- 
ever, the glass is very thick (Win high mag- 
nifiers), some of the rays which enter it will 
be reflected or sent back, and consequently 
the brilliancy of the image will suffer some 
diminution. 
A large object seen through a lens which 
is very convex will appear deformed ; and 
this proceeds from the refraction not being 
equal at all .points in such cases. The same 
cause operates also to render some parts of 
the image indistinct, wdiile others are distinct 
and clear. Thus the extremities of the 
image seen through a lens of a very short 
focus are commonly confused and indistinct, 
because the refraction at the edges of the lens 
does not agree with that of the m kid's parts. 
The modes adopted for remedying these de- 
fects in optical glasses, will be hereafter ex- ' 
plained. 
The effects of a concave lens are directly 
opposite to those of the convex lens. In 
other words, by such a glass, parallel rays 
are rendered divergent, converging rays have 
their convergence diminished, and diverging 
rays have their divergence augmented, in pro- 
portion to the concavjty of the lens. These 
glasses then exhibit objects smaller than they 
really are ; for by causing the rays to diverge, 
or more properly by diminishing the con- 
vergence of tiie rays proceeding from the ex- 
treme points of the object, the visual angle is 
rendered more acute, and the image painted 
on the retina is smaller, than it would have 
been had these rays not been intercepted in 
their natural progress; and by the diver- 
gence of the rays the object is represented 
with less clearness than it would otherwise 
have had, since from this cause a less quantity 
of light enters the pupil of the eye. All 
concave lenses have a negative or virtual fo- 
cus, which is a point corresponding with the 
divergence of parallel rays incident on the 
surface of the lens. 
Light is, however, not so simple a sub- 
stance as it may be supposed upon superfi- 
cially considering its general effects ; it is in- 
deed found to consist of particles which are 
differently refrangible, that is, some of them 
may be refracted more than others in passing 
through certain mediums, whence they are 
supposed by philosophers to be different in 
size. The common optical instrument called 
a prism, is a triangular piece of glass, through 
which if a pencil or collection of rays is made 
to pass, it is found that the rays do not pro- 
ceed parallel to each other on their emer- 
gence, but produce on an opposite wall, or 
any plane surface that receives them, an ob- 
long spectrum, which is variously coloured, 
and it consequently follows that some of the 
rays or particles are more refrangible than 
others. 
The spectrum thus formed is, perhaps, the 
most beautiful object which any of the ex- 
periments of philosophy presents to our view. 
'I he lower part, which consists of the least re- 
frangible rays, is of a lively red ; which, 
higher up, by insensible gradations, becomes 
an orange; the orange, in the same manner, 
is succeeded by a yellow ; the yellow, by a 
green ; the green, by a blue; after which "fol- 
lows a deep blue or indigo; and lastly, a faint 
violet. 
Of Vision. There is not any part of the 
animal frame which displays in a more satis- 
factory manner to our reason, the wisdom and 
design ot our Creator, than the eye. Its 
anatomical structure is however explained 
under the articles Anatomy and Physio- 
logy. It is only necessary at present to con- 
sider it as an optical instrument. The ex- 
ternal coat or case, which forms the globe of 
the eye, is at the back part strong and opake : 
the fore part is thin and transparent, so as to 
admit readily the rays of light ; and it is there- 
fore called the cornea, from its resemblance 
to polished horn. It incloses three pellucid 
matters called the humours, which are of dif- 
ferent densities. That in the anterior part, 
immediately under the cornea, is called the 
aqueous humour; that immediately behind is 
