OPTICS. 
perpendicular. This refraction is greater 
or less, that is, the rays are more or less 
bent or turned aside from their course, as 
the second medium through which they 
pass is more or less dense than the first. 
Thus, for instance, light is more refracted in 
passing from air into glass, than from air into 
water ; glass being denser than water. And, 
in general, in any two given media, the sine 
of any one angle of incidence has the same 
ratio to the sine of tlie corresponding angle 
of refraction, as the sine of any other angle 
ofincidencehas to the sine of its correspond- 
ing angle of refraction. Hence, when the angle 
of incidence is increased, the corresponding 
angle of refraction is also increased ; be- 
cause the ratio of their sines cannot conti- 
nue the same, unless they be both increased ; 
and if two angles of incidence be equal, the 
angles of refraction will be equal. The 
angle of deviation must also vary with the 
angle of incidence. If a ray of light, A C, 
(fig. 2) pass obliquely out of air into glass, 
A D the sine of the angle of incidence 
A C D, is to N S, the sine of the angle of 
refraction N C S, nearly as 3 to 2 ; there- 
fore, supposing the sines proportional to the 
angles, the sine of FCL the angle of de- 
viation, is as the difference between A D 
and N S, that is, as 3 — 2, or 1, whence the 
sine of incidence is to the sine of the angle 
of deviation as 3 to 1. In like manner it may 
be shewn, that when the ray passes ob- 
liquely out of glass into air, the sine of the 
angle of incidence will be to that of de- 
viation, as NS to AD — NS, that is, as 
2 to 1. In passing out of air into water, the 
sine of the angle of incidence is to that of 
refraction, as 4 to 3, and to that of de- 
viation, as 4 to 4 — 3, or 1 ; and in passing 
out of water into air, the sine of the angle of 
incidence is to that of refraction, as 3 to 4, 
and to that of deviation, as 3 to 1. Hence 
a ray of light cannot pass out of water into 
air at a greater angle of incidence than 
48" 36', the sine of which is to radius as 
3 to 4. Out of glass into air the angle must 
not exceed 40° 11', because the sine of 
40° iT is to radius as 2 to 3 nearly ; conse- 
quently, when the sine has a greater pro- 
portion to the radius than that mentioned, 
(he ray will not be refracted. It must be 
observed, that when the angle is within the 
limit, for light to be refracted, some of the 
rays will be reflected. For tiie surfaces of 
all bodies are for the most part uneven, 
which occasions the dissipation of much 
light by the most transparent bodies ; some 
being reflected, and some refracted, by the 
VOL. V. 
inequalities on the surfaces. Hence a per- 
son can see through water, and his image 
reflected by it at the same time. Hence 
also, in the dusk, the furniture in a room 
may be seen by the reflection of a window, 
while objects that are without are seen 
through it. 
Upon a smooth board, about the centre C, 
describe acircle H O K P ; draw two diame- 
ters of the circle, O P, H K, perpendicular 
to each other; draw ADM perpendicular to 
O P ; cut off D T and C I equal to three- 
fourths D A ; through T I, drawT I S, cutting 
the circumference in S ; NS drawn from S 
perpendicularly upon O P, will be equal to 
D T, or three-fourths of D A. Then if pins 
be stuck perpendicularly at A, C, and S, 
and the board be dipped in the water as 
far as the line H K, the pin at S will appear 
in the same line with the pins at A and C. 
This shews, that the ray which comes from 
the pin S is so refracted at C, as to come to 
the eye along the line C A ; whence the 
sine of incidence A D is to the sine of re- 
fraction N S, as 4 to 3. If other pins weie 
fixed along C S, they would all appear in 
A C produced ; which shews tJiat the ray is 
bent at the surface only. The same may 
be shewn, at different inclinations of the in- 
cident ray, by means of a moveable rod 
turning upon the centre C, which always 
keep the ratio of the sines A D, N S, as 
4 to 3. Also the sun’s shadow, coinciding 
with A C, may be shewn to be refracted in 
the same manner. The image L, of a 
small object S, placed under water, is one- 
fourth nearer the surface than the object. 
And hence the bottom of a pond, river, Ac. 
is one-third deeper than it appears to a 
spectator. 
To prove the refraction of light in a dif- 
ferent way, take an upright empty vessel 
into a dark room ; make a small hole in the 
window-shutter, so that a beam of light may 
fall upon the bottom at a (fig. 4) where you 
may ma\te a mark. Then fill the b.ason 
with water, without moving it out of its 
place, and you will see that the ray, instead 
of falling upon a, will fall at b. If a piece 
of looking-glass be laid in the bottom of the 
vessel, the light will be reflected from it, 
and will be observed to suffer the same re- 
fraction as in coming in ; only in a contrary 
direction. If the water be made a little 
muddy, by putting into it a few drops of 
milk, and if the room be filled with dust, 
the' rays will be rendered much more visi- 
ble. The same may be proved by another 
experiment. Put a piece of money into 
E 
