air, and they consequently suffer a greater 
refraction than the rest. Thus a straight 
leaden pipe appears near the bottom of a 
deep water to be curved, and a flat bason 
seems deeper in the middle than near the 
sides. 
To ese laws of refraction is to be attri- 
buted tne difference between the real and the 
apnerent rising of the sun, moon, and stars, 
above the horizon. The horizontal refrac- 
tion s something more than half a degree, 
■ : nee tne sun and moon appear above 
f horizon when they are entirely below it. 
om the horizon the refraction continually 
decreases to the zenith. Refraction is in- 
oreased by the density ot the air, and conse- 
quently it is greater in cold countries than in 
iiot ; and it is also affected by the degree ot 
cold or heat in the same country. 
Parallel rays, if refracted, preserve their 
parallel direction both in entering and in 
paying out of a retracing medium, provided 
the two surfaces o. the retracting medium are 
parallel. The two rays, EA, EA, (Jig. 27.) 
after refraction, while they approach the per- 
pendiculars pp, continue parallel as before, 
the reason of which is evident on the prin- 
ciples already established; lor the ray AC, 
(Pi. II. fig 3.) oncoming in contact with the 
surface ot the refracting medium EE, does not 
continue its course in the straight line C b, but 
being refracted at the point of contact C, it 
approaches the perpendicular Pp, and comes 
out at a. 
After coming out of the refracting medium, 
if we suppose the surface GH parallel to EF, 
it ought to proceed to B, having deviated 
from the perpendicular in the same degree in 
which it approached it on its first refraction ; 
and thus it continues parallel to the line CB, 
which is that in which it would have pro- 
ceeded if it had not been intercepted by the 
medium. 
This parallelism cannot subsist if the two 
surfaces Kf, HI, (fig. 4.) are inclined, as in 
the figure ; because the ray entering at a, and 
emerging at b, the object A will be seen from 
the point B at e, which is out of its true place. 
Converging rays become less convergent in 
passing from a rare to a denser medium, as 
from air into water; and on the contrary, 
their convergence is augmented by passing 
from a. dense to a rarer medium, as from wa- 
ter into air. (See fig. 1.) In the same man- 
ner, diverging rays become less divergent in 
passing out of a rare medium into one which 
is denser, and their divergence is increased by 
passing out of a dense into a rarer medium. 
(See fig. 2.) This fact is a necessary conse- 
quence of the general law of refraction : but 
it will -satisfactorily explain why an object 
under water appears larger to an eye above 
the surface than it really is, and why all ob- 
jects appear magnified seen through a mist; 
for in ail these cases, the converging rays, by 
which we see the extreme points of the ob- 
ject, and which during their passage through 
the water, See. were refracted towards the 
perpendicular, on their emergence into the 
air are made more suddenly to converge, and 
consequently the visual angle is rendered 
more obtuse. 
It i. evident, that when parallel rays fall 
upon a spherical surface, that ray only which 
E enet rates to the centre or axis will proceed 
i a direct course ; for all the rest muStneces- 
OPTICS. 
sarily make an angle more or -less obtuse, in 
proportion to their distance frdfh' the centre ; 
they are therefore rendered Convergent or 
divergent according to the nature of the me- 
dium on which they are incident. If they fall 
on the convex surface of a medium denser 
than that which they leave, as in passing 
from air into glass, they will converge, as may 
be seen in Plate II. fig. 5. where that phe- 
nomenon is represented ; for the parallel 
rays, ki,fg, (fig. 10.) falling in an oblique di- 
rection on the refracting medium terminated 
by the convex surface E/g, they will be re- 
tracted, and will each respectively approach 
the perpendiculars iC, orgC, and will conse- 
quently have a tendency to unite towards the 
axis All. 
It is however proper to remark, that the 
point at which they join the axis AB will be 
distant from the surface of the refracting me- 
dium, in proportion as the point on which they 
fall on the convex surface is distant from that 
axis; becau e the more distant that point is, 
the more oblique is the incidence of the ray. 
Finis the ray Id joins the axis at k ; but the 
ray fg does not join the axis till it arrives at D. 
Bays already convergent, falling on the 
convex surface of a dense medium, will be 
acted upon differently according to circum- 
stances. 
If their convergence is exactly propor- 
tioned to the convexity of the surface, they 
will not suffer any refraction ; (see fig. 6.) 
because in that case one of the essentials is 
wanting to refraction, viz. the obliquity of the 
incidence ; and each ray proceeds in a direct 
line to the centre of that circle, of which the 
convex surface is an arch or segment. 
For instance, the rays ef and dh, (fig. 1 1 .) 
which tend to unite at C, the centre of the 
convex surface, may be considered as per- 
pendicular, being the radii of thy circle. 
If the rays have a tendency to converge 
before they reach the centre of the convexity, 
they will then be rendered less convergent 
for instead of converging to a point at b 
(fig. 7.), they will converge at B. The rea- 
son of this is evident ; for the ray ih (fig. 11.) 
which, if not intercepted, would meet the 
axis at k, nearer the surface of the refracting 
medium than the centre of convexity C, be- 
ing refracted towards the perpendicular or 
radius dC, meets the axis only at o. 
If, on the contrary, the rays have a tend- 
ency to converge beyond the centre of the 
convexity, they will then, by the law of re- 
h action, be rendered still more convergent, 
as in fig. 8 ; where their point of union, if not 
intercepted, would be c ; but where, by the 
influence of the refraction, they are found to 
converge at C. For the ray gh, (fig. 1 1.) the 
tendency of which is towards /, is refracted 
towards the perpendicular dC, and joins the 
axis at p. 
If diverging rays fall on the convex surface 
of a denser medium, they are always ren- 
dered less divergent, as in fig. 9. ; and they 
may be rendered parallel, or even conver- 
gent, according to the degree of divergence 
compared with the convexity of the refract- 
ing surface, on the principles already ex- 
plained. 
If rays pass from a dense to a rarer medi- 
um, the surface of the dense medium being 
convex, in this case parallel rays become con- j 
vergent ; for the parallel rays de, gi, (fig. 12.) ! 
301 
when they reach the convex surface cD i, in- 
stead of continuing their direct course, arc 
refracted from the perpendiculars aC. bC, 
and converge at k. 
Converging rays are also rendered more 
convergent. Thus the rays le, ui, which 
without any change in the medium, would 
have proceeded in the direction rn and o, in 
consequence of the refraction which they 
suffer, and which bends them from the per- 
pendiculars aC, bC, unite at p. 
Diverging rays, if they proceed from the 
point C, the centre of convexity, suffer no 
refraction ; because, for the reasons already 
assigned, they may be considered as perpen- 
dicular to the refracting surface, and conse- 
quently they are deficient in one of the 
causes of refraction, the obliquity of inci- 
dence. 
If they proceed from a point which is 
nearer to the surface than the centre of con- 
vexity, such as r, they will be refracted from 
the perpendiculars aC, bC, and will be ren- 
dered more divergent towards x and ?/. 
If, on the contrary, the diverging rays 
come from a point such as q, beyond the cen- 
tre of convexity, they will be rendered less 
divergent; for instead of going towards z and 
z, they will be refracted from the perpendicu- 
lars a C, bC, towards/and h. 
When rays pass from a rare into a dense 
medium, and the surface of the dense medium 
is concave, then parallel rays are rendered 
divergent, as in Plate II. fig. 13. ; for the pa- 
rallel rays ab, de, (fig. 17.) are refracted to- 
wards the perpendiculars /C and gC, and 
are consequently divergent. 
Converging rays falling on the same con- 
cave surface will be rendered less conver- 
gent, as in fig. 14. For the rays ab, de, (fig. 
1 8.) which would have converged at O if their 
progress had not been intercepted, will be 
refracted towards the perpendiculars /C and 
gC, and will unite only at i. If the conver- 
gence was less, they might by the refraction 
be rendered parallel, or even divergent. 
Diverging rays proceeding from the centre 
of concavity will not suffer any refraction, for 
the reasons already assigned. 
If, however* diverging rays proceed from 
any point nearer the refracting surface than 
the centre of concavity, they will be rendered 
less divergent, as in tig. 15. For the two di- 
verging rays kb and ice (tig. 19.), instead of 
proceeding to d and h, are refracted towards 
the perpendiculars /C and gC. 
If, on the contrary, which is the most ge- 
neral case, the diverging rays proceed from a. 
point more distant from the surface than the 
centre of concavity, their divergence will be 
increased, as in fig. 16. For the diverging 
rays lb and le (fig. 19.), which tend towards 
m and n, are refracted towards the perpendi- 
culars JC and gC, and become more diver- 
gent than they would otherwise have been. 
When rays pass from a dense into a rarer 
medium, and the dense medium is terminated 
by a concave surface, then 
Parallel rays become divergent; for the 
parallel rays de, gi, (fig. 20..) when they reach 
the concave surface <T)f, instead of continu- 
ing their course in the direct lines towards f 
an dli, proceed towards m and p, being re- 
fracted from the perpendiculars C a, C b, anct 
are consequently divergent.. 
