OPTICS. 
o'Ow 
M, N, Sic. within the space of; which will in 
this direction diminish considerably the di- 
mensions of the image, according to the 
principles already explained in treating of 
the convex mirror, viz. by diminishing the 
convergence of rays, and consequently re- 
ducing the size of the image in proportion to 
the convexity. In the cylindrical mirror, it 
must be observed, that it is in the breadth 
only that this diminution takes place. The 
same will take place with respect to all the 
points ot die object which are visible within 
the lines BQG, CRH, DTI, ESK, concen- 
tric to the surface of the mirror. These parts 
must therefore be very much extended in 
the drawing or design, if a perfect image is to 
be represented in the mirror. Distorted 
drawings of this kind are common in the 
shops of the opticians, which, on a cylindri- 
cal mirror being placed on the board or draw- 
ing, display perfect figures. The principle 
ot these will, however, be very easily under- 
stood from, what lias been now stated. 
1 he conical mirror is represented in fig. 
22, and this is also considered as a mixed 
mirror; for, as well as the cylindrical, it pro- 
duces at once the effects of a convex and a 
plane mirror. Suppose, for instance, the 
angle CKF (fig. 23.) to. represent this mir- 
ror, anti the lines CK, FK, two of the right 
lines which compose it. These two lines 
would then answer to two plane mirrors in- 
clined towards each other : and the rays pro- 
ceeding from the points ABC, falling on 
the surface at g, h, i, and reflected to- 
wards the eye at O, would represent these 
points as if at the base of the mirror in the 
opposite order a, b, c ; and the same obser- 
vation will apply to the points D, E, F, which 
are represented at d, e,f, as well as all those 
which are in the circles AI1D, B1E, CGF. 
But as there do not proceed from each point 
simple rays of light, but pencils ofYays, they 
are modified in this mirror upon the same 
principles as in the convex mirror; and con- 
sequently the image will appear smaller than 
the object, and nearer to the eye, than in the 
plane mirror. 
Hence it will be evident, that we mav see 
in the centre the image of whatever is painted 
on the exterior circumference AHD, and the 
extremities of the image will be formed from 
interior circle CGF; and as the curva- 
ture or convexity of. the mirror is greater to' 
wards the apex or point of the cone, it fol- 
low's, that that which is the most extended in 
the object will be the most compressed or 
concentrated in the image. Thus the dark 
part ot the board (lig. 24.) is intended to re- 
present in the mirror an ace of spades ; and 
the points a, b, <■, d, c,f, g, &c. which are 
nearest to the mirror, form the outer circum- 
ference of the image; and the points 1, 2,3, 
4, 5, 0, 7, 8, of the external circumference 
of the board, unite in (lie centre of the image 
at an almost imperceptible point. 
Of the refraction of light, or dioptrics. 
.It has been proved that light, like every 
known substance, is subject to the laws of at- 
traction ; it has been intimated too, that even 
its propensity to move in a direct line is, in 
certain cases, overcome by this superior in- 
fluence; and that the direction of the rays of 
light is changed in passing from one medium 
to another. The space in which a ray of 
light moves is called amedinm ; whether pure i 
soace, air,’ water, glass, or any other trails- I 
8 
parent substauce ; and when a ray is bent 
out of its natural course in passing from one 
medium to another, it is said to be refracted 
or broken, probably from the broken appear- 
ance which a staff, &c. exhibits when part of 
it is immersed in water. 
There are two circumstances essential to 
refraction: 1st, That the rays of light shall 
pass out of one medium into another of a dif- 
ferent density, or of a greater or less degree 
of resistance. 2dly, That they pass in an 
oblique direction. 
The denser the refracting medium, or that 
into which the ray passes, is, tiie greater will 
be its refracting power ; and of 1 wo refracting 
mediums of the same density, that which is of 
an oily or inflammable nature will have a 
greater refracting power than the other. 
The angle of refraction depends on the ob- 
liquity of the rays falling on the refracting 
surface being such always, that the sine of the 
incident angle is to the sine of the refracted 
angle in a given proportion. 
The incident angle is the angle made by a 
ray of light, and a line drawn perpendicular to 
the refracting surface, at the point where the 
light enters the surface ; and the refracted 
angle is the angle made by the ray in the re- 
fracting medium with the same perpendicular 
produced. The sine of the angle is a line 
which serves to measure the angle, being 
drawn from a point in one leg perpendicular 
to the other. 
In passing from a rare into a dense medi- 
um, or from one dense medium into a denser 
medium, a ray of light is refracted towards 
the perpendicular, that is, so that the angle of 
refraction shall be less than the angle of inci- 
dence ; on the contrary, in passing from a 
dense medium into a rare medium, or from 
one rare medium into a rarer, a ray of light 
is refracted from the perpendicular. Thus, 
in passing from empty space into air, or any 
otiier medium whatever, the ray is bent 
towards the perpendicular ; and in passing 
from any oilier medium into pure space, it is 
bent the contrary way, that is, from the per- 
pendicular; the same effects will take place 
in passing from air into glass, and from glass 
into air, &c. 
To render this perfectly clear, let us have 
recourse to fig. 25. If a ray of light pG 
passes from air to water, in the direction 
pG, perpendicular to the plane I)<Z, which se- 
parates the two mediums, it suffers no re- 
fraction, because one of the essentials is 
wanting to that effect, viz. the obliquity of 
the incidence. 
I But if a ray AG passes obliquely from air 
into water, instead of continuing its course in 
the direct line GB, it takes the direction Go, 
and approaches the perpendicular pP, in such 
a manner that the angle of refraction PGa is 
less than its angle of incidence pG A. 
If the ray came in a more oblique direc- 
tion, the refraction would be still greater; so 
that in all cases where the mediums are the 
same, the angle of refraction will always be 
found to bear a regular and constant propor- 
tion to the angle of incidence ; or, to speak 
in technical language, the sine of incidence is 
to the sine of refraction in a given ratio, and 
this ratio is discovered bv experience. Thus, 
when a ray passes out of air into water, the 
ratio is as 4 to 3. 
•ut of water into air, as 3 to 4. 
air into glass, as 3 to 2. 
glass into air, as 2 to 3. 
air into diamond, as 5 to 2. 
diamond into air, as 2 to 5. 
I ne retraction of light is attributed bv sir 
Isaac IS ewton to the principle of attraction: 
. pClh ; 1|)S ? lie ot the most satisfactory 
pioots o, this theory is the known fact, that 
the change in the direction of the rav com- 
mences, not when it conies in contact with 
t tie l enacting medium, but a little before it 
reacnes the surface, and the incurvation aug- 
mentsu 1 proportion as it approaches thisme- 
‘ nil. Indeed no principle wii! account for 
4 c phenomenon of light passing more easily, 
dlrectl y> through a dense than 
plough a rare medium, but that of altrac- 
1011 ’ ® 1Ilce ’t is found tby universal experi- 
ence, that the attraction of all bodies is in 
proportion to their densities. 
In passing from a dense into a rare 
Zvrr er i^ is a certain degree of ob- 
•quity at which the refraction is changed 
into reflection. In other words, a rav" of 
light will not pass out of a dense into a'rare 
meduim, if the angle of incidence exceeds a 
certain limit, but will be reflected back 
thus a ray of light will not pass out of glass 
into air, if t he angle of incidence exceeds 40 * 
. 5 or ol| t °I glass into water, if the angle of 
incidence exceeds 59° 20. 
As tne rays of light, in passing from a dense 
medium to a rarer, are refracted from the 
perpendicular, in fact are bent or inclined 
towards the eye of the spectator, who looks 
at an object in the denser medium while 
standing at its side, the reason will be clear 
wiiy the bottom of a river appears to us 
neaiei than it really is. If the spectator 
stands on a bank just about the level of the 
water, it is about one-third deeper than it ap- 
pears ; and why an oar, partly in and partly 
I out of the water, seems broken. Let Q no 
\ (bg. 26.) represent an oar, the part nQ being 
out of, and the part no being in, the water* 
the rays diverging from o will appear to di- 
verge from b nearer to the surface of the 
water, and every point in no will be found 
nearer to the surface than its real place, and 
the part no will appear to make an angle 
with the part Q n. On this account also, a 
hsh in the water appears much nearer the 
surface than it actually is; and a skilful 
maiksman, in shooting at it, will aim con- 
siderably below the place which it seems to- 
occupy. 
On the same principle a common experi- 
ment is explained. Put a shilling into a ba- 
son, and walk back from it till the shilling is 
just obscured by the side of the bason; then 
by pouring water into the bason, the shilling 
instantly appears; for by what has been said 
above, the object, being now in a denser me- 
dium, is made to appear nearer to its surface. 
As the refraction must in all cases depend 
on the obliquity of the ray, that part of any 
body which is most immersed will seem to be 
most materially altered by the refraction. 
When, however, the object extends to no 
great depth in the water, the figure is not ma- 
terially distorted ; but if the object is of a 
considerable size, or extends ' to a great 
depth, those rays which proceed from the 
more distant extremities come in a more ob- 
lique direction on their emergence into the. 
