Encyclopaedia Britannica > Volume 15, NIC-PAR

Theory. OPT
Of gree.9, lias enabled us to employ much larger portions
iAberration, of the sphere than Mr Dollond could introduce into his
n_' object-glasses, it becomes absolutely necessary to study
this matter completely, in order to discover and ascer¬
tain the amount of the errors which perhaps unavoid-
203 ably remain.
icontrary This slight sketch of the most simple case of aber-
~S ration> namely, when the incident rays are parallel,
each other, will serve to give a general notion of the subject; and
the reader can now see how contrary aberrations may
be employed in order to form an ultimate image which
shall be as distinct as possible. For let it be proposed
Plate to converge parallel rays accurately to the focus F,
6&3.VI' tbe refratti°n °f spherical surfaces of which V
is the vertex. Let PV be a convex lens of such a
form, that rays flowing from F, and passing through it
immediately round the vertex V, are collected to the
eonjugate focus R, while the extreme ray FP, inci¬
dent on the margin of the lens P, is converged to r,
nearer to V, having the longitudinal aberration R r.
Let V be a plano-concave lens, of such sphericity
that a ray A jj, parallel to the axis CV, and incident
on the point as far from its vertex V as P in the
other lens is from its vertex, is dispersed from r, the
distance 5 V being equal to s V, while the central ravs
are dispersed fiom P, as far from V as R is from V.
It is evident, that if these lenses be joined as in fig. 4.
a ray A’/>, parallel to the common axis CV, will be
collected at the distance VF equal to VF in the fig. 4.
and that rays passing through both lenses in the neigh¬
bourhood of the axis will be collected at the same
point F.
This compound lens is said to be without spheri¬
cal aberration ; and it is true that the central and the
extreme rays are collected in the same point F: but
the rays which fall on the lens between the centre and
margin are a little diffused from F, and it is not pos¬
sible to collect them all to one point. For in the rules
for computing the aberration, quantities are neglected
which do not preserve, in different apertures, the same
ratio to the quantities retained. The diffusion is least
when the aberration is corrected, not for the very ex¬
tremity, but for a certain intermediate point (varying
with the aperture, and having no known ratio to it) j
and when this is done, the compound lens is in its state
of greatest perfection, and the remaining aberration is
quite insensible. See Telescope.
Sect. VI. 0« different Refrangibility of Light.
As this property of light solves a great number of the
phenomena which could not be understood by former
opticians, we shall give an account of it nearly in the
words of Sir Isaac Newton, who first discovered it j es¬
pecially as his account is more full and perspicuous than
those of succeeding writers.
Kate ** -^n a dark chamber, at a round hole F, about one
erxEsm.third of an inch broad, made in the shutter of a window,
1. I placed a glass prism ABC, whereby the beam of the
sun’s light, SF, which came in at that hole, might be
refracted upwards, toward the opposite wall of the cham¬
ber,and there form a coloured image of the sun, repre¬
sented at PT. The axis of the prism was, in this and
the following experiments, perpendicular to the incident
rajs. About this axis I turned the prism slowly, and
I c s.
251
saw the refracted or coloured image of the sun, first to On the dif-
descend, and then to ascend. Between the descent and ferent re¬
ascent, when the image seemed stationary, I stopped the tran^ibility
prism and fixed it in that posture. 01 *^Rht-
“ Then I let the refracted light fall perpendicularly '
upon a sheet of white paper, MN, placed at the oppo¬
site wall of the chamber, and observed the figure and
dimensions of the solar image, FT, formed on the pa¬
per by that light. This image was oblong, and not
oval, but terminated by two rectilinear and parallel sides
and two semicircular ends. On its sides it was bounded,
pretty distinctly ; but on its ends very indistinctly, the
light there vanishing by degrees. At the distance of
18!- feet from the prism the breadth of the image was
about 2-g- inches, but its length was about 10^ inches,
and the length of its rectilinear sides about 8 inches ^
and ACB, the refracting angle of the prism, by which,
so great a length was made, was 64 degrees. \\ ith a
less angle the length of the image was less, the breadth
remaining the same. It is farther to be observed, that
the rays went on in straight lines from the prism to the
image, and therefore at their going out of the prism had
all that inclination to one another from which the length
of the image proceeded. This image FT was coloured,
and the more eminent colours lay in this order from
the bottom at I to the top at P j red, orange, yellow,
green, blue, indigo, violet $ together with all their in¬
termediate degrees in a continual succession perpetually
varying.”
Our author concludes from this and other ex peri- jjgbt con-
ments, “ that the light of the sun consists of a mixture sists of se-
of several sorts of coloured rays, some of which at equal ▼eral sorts
incidences are more refracted than others, and therefore of co*°”!et*
are called wore refrangible. The red at T, being near- rentlv re-'
est to the place Y, where the rays of the sun would sro frangibte,
directly if the prism was taken aw'ay, is the least refrac-
ed of all the range j and the orange, yellow, green, blue,
indigo, and violet, are continually more and more re¬
fracted, as they are more and more diverted from the
course of the direct light. For by mathematical rea¬
soning he has proved, that when the prism is fixed in
the posture above mentioned, so that the place of the
image shall be the lowest possible, or at the limit be¬
tween its descent and ascent, the figure of the image
ought then to be round like the spot at Y, if all the
rays that tended to it were equally refracted. There¬
fore, since it is found by experience that this image is
not round, but about five times longer than broad, it
follows, that all the rays are not equally refracted.
This conclusion is farther confirmed by the following
experiments.
“ In the sunbeam SF, which was propagated into the Fig- %•
room through the hole in the window-shutter EG, at
the distance of some feet from the hole, I held the prism
ABC in such a posture, that its axis might be perpendi¬
cular to that beam : then I looked through the prism
upon the hole F, and turning the prism to and fro about
its axis to make the image p £ of the hole ascend and
descend, when between its two contrary motions it
seemed stationary, I stopped the prism ; in this situation
of the prism, viewing through it the said hole E, I ob¬
served the length of its refracted image p £ to be many
times greater than its breadth $ and that the most re¬
fracted part thereof appeared violet at p ; the least re¬
fracted, at t ; and the middle parts indigo, blue, green,,
1 i 2 yellow,