A’s and B’s, and of the references to figures. When objects are viewed
through a flat or plane glass, the rays of light in passing through it,
from the object to the eye, proceed in a strait direction and parallel
to each other, and consequently the object appeared at the same distance
as to the naked eye, neither enlarged or diminished. But if the glass be
of a convex form, the rays of light change their direction in passing
through the glass, and incline from the circumference towards the center
of convexity, in an angle proportional to the convexity, and meet at a
point at a less or greater distance from the glass, as it is more or
less convex. The point where the rays thus meet is called the focus;
when, therefore, the convexity is small, the focus is at a great
distance, but when it is considerable, the focus is near; the magnifying
power is in proportion to the change made in the rays, or the degree of
convexity, by which we are enabled to see an object nearer than we
otherwise could; and the nearer it is brought to the eye, the larger
will be the angle under which it appears, and consequently the more it
will be magnified.
The human eye is so constituted, that it can only have distinct vision,
when the rays which fall on it are parallel, or nearly so; because the
retina, on which the image is painted, is placed in the focus of the
crystalline humor, which performs the office of a lens in collecting
rays, and forming the image in the bottom of the eye.
As an object becomes perceptible to us, by means of the image thereof
which is formed on the retina, it will, therefore, be seen in that
direction, in which the rays enter the eye to form the image, and will
always be found in the line, in which the axis of a pencil of rays
flowing from it enters the eye. We from hence acquire a habit of judging
the object to be situated in that line. Note; as the mind is
unacquainted with the refraction the rays suffer before they enter the
eye, it judges them to be in the line produced back, in which the axis
of a pencil of rays flowing from it is situated, and not in that in
which it was before the refraction.
If the rays, therefore, that proceed from an object, are refracted and
reflected several times before they enter the eye, and these refractions
or reflections change considerably the original direction of the rays
which proceed from the object, it is clear, that it will not be seen in
that line, which would come strait from it to the eye; but it will be
seen in the direction of those rays which enter the eye, and form the
image thereof on it.
We perceive the presence and figure of objects, by the impression each
respective image makes on the retina; the mind, in consequence of these
impressions, forms conclusions concerning the size, position, and motion
of the object. It must however be observed, that these conclusions are
often rectified or changed by the mind, in consequence of the effects of
more habitual impressions. For example, there is a certain distance, at
which, in the general business of life, we are accustomed to see
objects: now, though the measure of the image of these objects changes
considerably when they move from, or approach nearer to us, yet we do
not perceive that their size is much altered; but beyond this distance,
we find the objects appear to be diminished, or increased, in proportion
as they are more or less distant from us.
For instance, if I place my eye successively at two, at four, and at six
feet from the same person, the dimensions of the image on the retina
will be nearly in the proportion of 1, of ¹⁄₂, of ¹⁄₃, and consequently
they should appear to be diminished in the same proportion; but we do
not perceive this diminution, because the mind has rectified the
impression received on the retina. To prove this, we need only consider,
that if we see a person at 120 feet distance, he will not appear so
strikingly small, as if the same person should be viewed from the top of
a tower, or other building 120 feet high, a situation to which we had
not been accustomed.
From hence, also, it is clear, that when we place a glass between the
object and the eye, which from its figure changes the direction of the
rays of light from the object, this object ought not to be judged as if
it were placed at the ordinary reach of the sight, in which case we
judge of its size more by habit than by the dimensions of the images
formed on the retina; but it must be estimated by the size of the image
in the eye, or by the angle formed at the eye, by the two rays which
come from the extremity of the object.
If the image of an object, formed after refraction, be greater or less
than the angle formed at the eye, by the rays proceeding from the
extremities of the object itself, the object will appear also
proportionably enlarged or diminished; so that if the eye approach to or
remove from the last image, the object will appear to increase or
diminish, though the eye should in reality remove from it in one case,
or approach toward it in the other; because the image takes place of the
object, and is considered instead of it.
The apparent distance of an object from the eye, is not measured by the
real distance from the last image; for, as the apparent distance is
estimated principally by the ideas we have of their size, it follows,
that when we see objects, whose images are increased or diminished by
refraction, we naturally judge them to be nearer or further from the
eye, in proportion to the size thereof, when compared to that with which
we are acquainted. The apparent distance of an object is considerably
affected by the brightness, distinctness, and magnitude thereof. Now as
these circumstances are, in a certain degree, altered by the refraction
of the rays, in their passing through different mediums, they will also,
in some measure, affect the estimation of the apparent distance.
In the theory of vision it is necessary to be cautious not to confound
the organs of vision with the being that perceives, or with the
perspective faculty. The eye is not that which sees, it is only the
organ by which we see. A man cannot see the satellites of Jupiter but by
a telescope. Does he conclude from this, that it is the telescope that
sees those stars? By no means; such a conclusion would be absurd. It is
no less absurd to conclude, that it is the eye that sees. The telescope
is an artificial organ of sight, but it sees not. The eye is a natural
organ of sight, by which we see; but the natural organ sees as little as
the artificial.
The eye is a machine, most admirably contrived for refracting the rays
of light, and forming a distinct picture of objects upon the retina; but
it sees neither the object nor the picture. It can form the picture
after it is taken out of the head, but no vision ensues. Even when it is
in its proper place, and perfectly sound, it is well known, that an
obstruction in the optic nerve takes away vision, though the eye has
performed all that belongs to it.[25]
[25] Reid on the Intellectual Powers of Man, p. 78.
OF THE SINGLE MICROSCOPE.
The single microscope renders minute objects visible, by means of a
small glass globule, or convex lens, of a short focus. Let E Y, Fig. 11.
Plate I. represent the eye; and O B a small object, situated very near
to it; consequently, the angle of its apparent magnitude very large. Let
the convex lens R S be interposed between the eye and the object, so
that the distance between it and the object may be equal to the focal
length; and the rays which diverge from the object, and pass through the
lens, will afterwards proceed, and consequently enter the eye parallel:
after which, they will be converged, and form an inverted picture on the
retina, and the object will be clearly seen; though, if removed to the
distance of six inches, its smallness would render it invisible.
When the lens is not held close to the eye, the object is somewhat more
magnified; because the pencils, which pass at a distance from the
center of the lens, are refracted inward toward the axis, and
consequently seem to come from points more remote from the center of the
object, as may be seen in Fig. 12. Plate I. where the pencils which
proceed from O and B are refracted inwards, and seem to come from the
point i and m.
Fig. 8. Plate I. may, perhaps give the reader a still clearer view, why
a convex lens increases the angle of vision. Without a lens, as F G, the
eye at A would see the dart B C under the angle b A c; but the rays B F
and C G from the extremities of the dart in passing through the lens,
are refracted to the eye in the directions f A and g A, which causes the
dart to be seen under the much larger angle D A E (the same as the angle
f A g.) And therefore the dart B C will appear so much magnified, as to
extend in length from D to E.
The object, when thus seen distinctly, by means of a small lens, appears
to be magnified nearly in the proportion which the focal distance of the
glass bears to the distance of the objects, when viewed by the naked
eye.
To explain this further, place the eye close to the glass, that as much
of the object may be seen at one view as is possible; then remove the
object to and fro, till it appear perfectly distinct, and well defined;
now remove the lens, and substitute in its place a thin plate, with a
very small hole in it, and the object will appear as distinct, and as
much magnified, as with the lens, though not quite so bright; and it
appears as much more magnified in this case, than it does when viewed
with the naked eye, as the distance of the object from the hole, or
lens, is less than the distance at which it may be seen distinctly with
the naked eye.
From hence we see, that the whole effect of the lens is to render the
object distinct, which it does by assisting the eye to increase the
refraction of the rays in each pencil; and that the apparent magnitude
is entirely owing to the object being seen so much nearer the eye than
it could be viewed without it.
Single microscopes magnify the diameter of the object,[26] as we have
already shewn, in the proportion of the focal distance (to the limits of
distinct vision with the naked eye) to eight inches. For example, if the
semi-diameter of a lens, equally convex on both sides, be half an inch,
which is also equal to its focal distance, we shall have as ¹⁄₂ is to 8,
so is 1 to 16; that is, the diameter of the object in the proportion of
sixteen to one. 2. As the distance of eight inches is always the same,
it follows, that by how much the focal distance is smaller, there will
be a greater difference between it and the eight inches; and
consequently, the diameter of the object will be so much the more
magnified, in proportion as the lenses are segments of smaller spheres.
3. If the object be placed in the focus of a glass globule or sphere,
and the eye be behind it in the focus, the object will be seen distinct
in an erect situation, and magnified as to its diameter, in the
proportion of ³⁄₄ of the diameter of the globule to eight inches; thus
suppose the diameter of the sphere to be ¹⁄₁₀ of an inch, then ³⁄₄ of
this will be equal to ³⁄₄₀; consequently, the real diameter of the
object to the apparent one, as ³⁄₄₀ to 8, or as 3 to 320, or as 1 to 106
nearly.
[26] Cyclopedia, Article Microscope.
OF THE DOUBLE OR COMPOUND MICROSCOPE.
In the compound microscope, the image is viewed instead of the object,
which image is magnified by a single lens, as the object is in a single
microscope. It consists of an object lens N L, Fig. 5. Plate I. and an
eye glass F G. The object B O is placed a little further from the lens
than its principal focal distance, so that the pencils of rays
proceeding from the different points of the object through the lens, may
converge to their respective foci, and form an inverted image of the
object at Q P; which image is viewed by the eye through the eye glass F
G, which is so placed, that the image may be in its focus on one side,
and the eye at the same distance on the other. The rays of each pencil
will be parallel, after passing out of the glass, till they reach the
eye at E, where they will begin to converge by the refractive powers of
the humours; and after having crossed each other in the pupil, and
passed through the crystalline and vitreous humours, they will be
collected in points on the retina, and form a large inverted image
thereon.
It will be easy, from what has been already explained, to understand the
reason of the magnifying power of a compound microscope. The object is
magnified upon two accounts; first, because if we viewed the image with
the naked eye, it would appear as much larger than the object, as the
image is really larger than it, or as the distance f R is greater than
the distance f b; and secondly, because this picture is again magnified
by the eye glass, upon the principle explained in the foregoing article
on vision, by single microscopes.
But it is to be noted, that the image formed in the focus of a lens, as
is the case in the compound microscope, differs from the real object in
a very essential particular; that is to say, the light being emitted
from the object in every direction, renders it visible to an eye placed
in any position; but the points of the image formed by a lens, emitting
no more than a small conical body of rays, which arrives from the glass,
can be visible only when the eye is situate within its confine. Thus,
the pencil, which emanates from o in the object, and is converged by
the lens to D, proceeds afterwards diverging towards H, and, therefore,
never arrives at the lens F G, nor enters the eye at E. But the pencils
which proceed from the points o and b, will be received on the lens F G,
and by it carried parallel to the eye; consequently, the correspondent
points of the image Q P will be visible; and those which are situate
farther out towards H and I, will not be seen. This quantity of the
image Q P, or visible area, is called the field of view.
Hence it appears, that if the image be large, a very small part of it
will be visible; because the pencils of rays will for the most part fall
without the eye glass F G. And it is likewise plain, that a remedy which
would cause the pencils, which proceed from the extremes B and O of the
object, to arrive at the eye, will render a greater part of it visible:
or, in other words, enlarge the field of view. This is effected by the
interposition of a broad lens D E, Fig. 5, of a proper curvature, at a
small distance from the focal image. For, by those means, the pencil D
N, which would otherwise have proceeded towards H, is refracted to the
eye, as delineated in the figure, and the mind conceives from thence the
existence of a radiant point at Q, from which the rays last proceeded.
In like manner, and by a parity of reason, the other extreme of the
image is seen at P, and the intermediate points are also rendered
visible. On these considerations it is, that compound microscopes are
usually made to consist of an object lens N L, by which the image is
formed, enlarged, and inverted; an amplifying lens D E, by which the
field of view is enlarged, and an eye glass or lens, by which the eye is
allowed to approach very near, and consequently to view the image under
a very great angle of apparent magnitude. It is now customary to combine
two or more lenses together at the eye glass, in the manner of Eustachio
Divinis and M. Joblot; by which means the aberration of light from the
figure is in some measure corrected, and the apparent field increased.
OF THE SOLAR MICROSCOPE.
In this instrument, the image of the object is refracted upon a screen
in a darkened room. It may be considered under two distinct heads: 1st,
the mirror and lens, which are intended to reflect and transmit the
light of the sun upon the object; and 2dly, that part which constitutes
the microscope, or which produces the magnified image of the object,
Fig. 10. Plate I. Let N O represent the side of a darkened chamber, G H
a small convex lens, fixed opposite to a perforation in the side N O, A
B a plane mirror or looking glass, placed without the room to reflect
the solar rays on the lens C D, by which they are converged and
concentrated on the object fixed at E F.
2. The object being thus illuminated, the ray which proceeds from E will
be converged by the lens G H to a focus K, on the screen L M; and the
ray which comes from F will be converged to I, and the intermediate
points will be delineated between I and K; thus forming a picture, which
will be as much larger than the object, in proportion as the distance of
the screen exceeds that of the image from the object; a small object,
such as a mite, &c. may be thus magnified to eight or ten feet in
diameter.
From what has been said, it appears plainly, the advantages we gain by
microscopes are derived, first, from their magnifying power, by which
the eye is enabled to view more distinctly the parts of minute objects:
secondly, that by their assistance, more light is thrown into the pupil
of the eye, than is done without them. The advantages procured by the
magnifying power, would be exceedingly circumscribed, if they were not
accompanied by the latter: for if the same quantity of light be
diffused over a much larger surface, its force is proportionably
diminished; and therefore the object, though magnified, will be dark and
obscure. Thus, suppose the diameter of the object to be enlarged ten
times, and consequently the surface one-hundred times, yet, if the focal
distance of the glass were eight inches, provided this were possible,
and its diameter only about the size of the pupil of the eye, the object
would appear one-hundred times more obscure when viewed through the
glass, than when it was seen by the naked eye; and this even on the
supposition that the glass transmitted all the light which fell upon it,
which no glass can do. But if the glass were only four inches focal
distance, and its diameter remained as before, the inconvenience would
be vastly diminished, because the glass could be placed twice as near
the object as before, and would consequently receive four times as many
rays as in the former case, and we should, therefore, see it much
brighter than before. By going on thus, diminishing the focal distance
of the glass, and keeping its diameter as large as possible, we shall
perceive the object proportionably magnified, and yet remain bright and
distinct. Though this is the case in theory, yet there is a limit in
optical instruments, which is soon arrived at, but which cannot be
passed. This arises from the following circumstances.[27]
[27] Encyclopædia Britannica, last edition, vol. xiii, p. 357.
1. The quantity of light lost in passing through the glass.
2. The diminution in the diameter of the glass or lens itself, by which
it receives only a small quantity of rays.
3. The extreme shortness of the focal distance of great magnifiers,
whereby the free access of the light to the object we wish to view is
impeded, and consequently the reflection of the light from it is
weakened.
4. The aberration of the rays, occasioned by their different
refrangibility.
To make this more clear, let us suppose a lens made of such dull kind of
glass, that it transmits only one half the light that falls upon it. It
is evident, that supposing this lens to be of four inches focus, and to
magnify the diameter of the object twice, and its own breadth equal to
that of the pupil of the eye, the object will be four times magnified in
surface, but only half as bright as if it was seen by the naked eye at
the usual distance; for the light which falls upon the eye from the
object at eight inches distance, and likewise the surface of the object
in its natural size, being both represented by 1, the surface of the
magnified object will be 4, and the light which makes it visible only 2;
because, though the glass receives four times as much light as the naked
eye does at the usual distance of distinct vision, yet one half is lost
in passing through the glass. The inconvenience, in this respect, can
only be removed so far as it is possible to increase the transparency of
the glass, that it may transmit nearly all the rays which fall upon it;
and how far this can be done, has not been yet ascertained.
The second obstacle to the perfection of microscopic glasses, is the
small size of great magnifiers; by which means, notwithstanding their
near approach to the object, they receive a smaller quantity of light
than might be expected. Thus, suppose a glass of only one-tenth of an
inch focal distance, such a glass would increase the visible diameter
eighty times, and the surface 6400 times. If the breadth of the glass
could at the same time be preserved as great as the pupil of the eye,
which we shall suppose one-tenth of an inch, the object would appear
magnified 6400 times, and every part would be as bright as it appears to
the naked eye. But if we suppose the lens to be only ¹⁄₂₀ of an inch
diameter, it will then only receive one-fourth of the light which would
otherwise have fallen upon it; therefore, instead of communicating to
the magnified object a quantity of light equal to 6400, it would
communicate an illumination suited only to 1600, and the magnified
object would appear four times as dim as it does to the naked eye. This
inconvenience can, however, in a great degree be removed, by throwing a
much larger quantity of light on the object. Various methods of
effecting this purpose will be pointed out in the course of this work.
The third obstacle arises from the shortness of the focal distance in
large magnifiers; this inconvenience can, like the former, be remedied
in some degree, by artificial means of accumulating light; but still the
eye is strained, as it must be brought nearer the glass than it can well
bear, which in some measure supersedes the use of very deep lenses, or
such as are capable of magnifying beyond a certain degree.
The fourth obstacle arises from the different refrangibility of the rays
of light, which frequently causes such deviations from truth in the
appearance of things, that many have imagined themselves to have made
surprising discoveries, and have communicated them as such to the world;
when, in fact, they have been only so many optical deceptions, owing to
the unequal refraction of the rays. In telescopes, this error has been
happily corrected by the late Mr. Dollond’s valuable discovery of
achromatic glasses; but how far this invention is applicable to the
improvement of microscopes, has not yet been ascertained; and, indeed,
from some few trials made, there is reason for supposing they cannot be
successfully applied to microscopes with high powers; so that this
improvement is yet a desideratum in the construction of microscopes, and
they may be considered as being yet far from their ultimate degree of
perfection.[28]
[28] How many useful and ingenious discoveries have arisen from
accidental circumstances? To adduce one recent instance
only--Aerostation, a science, which after having baffled the skill and
ingenuity of philosophers for a series of years, and by many
illiterate persons deemed an idea bordering on absurdity, has been of
late discovered, and successfully applied to practice. EDIT.
OF THE MAGNIFYING POWERS OF THE MICROSCOPE.
We have already treated of the apparent magnitude of objects, and shewn
that they are measured by the angles under which they are seen, and that
this angle is greater or smaller according as the object is nearer to,
or further from, the eye; and, consequently, the less the distance at
which it can be viewed, the larger it will appear: but from the limits
of natural vision, the naked eye cannot distinguish an object that is
very near to it; yet, when assisted by a convex lens, distinct vision is
obtained, however short the focus of the lens, and, consequently, how
near soever the object is to the eye; and the shorter the focus of the
lens is, the greater will be the magnifying power thereof. From these
considerations, it will not be difficult to estimate the magnifying
power of any lens used as a single microscope; for this will be in the
same proportion that the limits of natural sight bear to the focus of
the lens. If, for instance, the convex lens is of one inch focus, and
the natural sight of eight inches, an object seen through that lens will
have its diameter apparently increased eight times; but, as the object
is increased in every direction, we must square this apparent diameter,
to know how much the object is really magnified; and thus multiplying 8
by 8, we find the superficies is magnified 64 times.
From these principles, the following general rule for ascertaining the
magnifying power of single lenses, is deduced. Place a small thin
transparent object on the stage of the microscope, adjust the lens till
the object appears perfectly distinct, then measure the distance
accurately between the lens and the object, reduce the measure thus
found to the hundredths of an inch, and calculate how many times this
measure is contained in eight inches, first reducing the eight inches
into hundredths, which will give you the number of times the diameter of
the object is magnified; which number multiplied into itself, or
squared, gives the apparent superficial magnitude of the object.