side of the house, is really in shadow; it is the west side, which the
sun cannot shine upon, till the afternoon.
_Emily._ Those objects, then, which are illumined by reflected rays, and
those which receive direct rays from the sun, but which do not reflect
those rays towards us, appear equally in shadow?
_Mrs. B._ Certainly; for we see them both illumined by reflected rays.
That part of the sheet of water, over which the trees cast a shadow, by
what light do you see it?
_Emily._ Since it is not by the sun's direct rays, it must be by those
reflected on it from other objects, and which it again reflects to us.
_Caroline._ But if we see all terrestrial objects by reflected light,
(as we do the moon,) why do they appear so bright and luminous? I should
have supposed that reflected rays, would have been dull and faint, like
those of the moon.
_Mrs. B._ The moon reflects the sun's light, with as much vividness as
any terrestrial object. If you look at it on a clear night, it will
appear as bright as a sheet of water, the walls of a house, or any
object seen by daylight, and on which the sun shines. The rays of the
moon are doubtless feeble, when compared with those of the sun; but that
would not be a fair comparison, for the former are incident, the latter,
reflected rays.
_Caroline._ True; and when we see terrestrial objects by moonlight, the
light has been twice reflected, and is consequently, proportionally
fainter.
_Mrs. B._ In traversing the atmosphere, the rays, both of the sun, and
moon, lose some of their light. For though the pure air, is a
transparent medium, which transmits the rays of light freely, we have
observed, that near the surface of the earth, it is loaded with vapours
and exhalations, by which some portion of them are absorbed.
_Caroline._ I have often noticed, that an object on the summit of a
hill, appears more distinct, than one at an equal distance in a valley,
or a plain; which is owing, I suppose, to the air being more free from
vapours in an elevated situation, and the reflected rays, being
consequently brighter.
_Mrs. B._ That may have some sensible effect; but, when an object on the
summit of a hill, has a back ground of light sky, the contrast with the
object, makes its outline more distinct.
_Caroline._ I now feel well satisfied, that we see opaque objects, only
by reflected rays; but I do not understand, how these rays, show us the
objects from which they proceed.
_Mrs. B._ I shall hereafter describe the structure of the eye, very
particularly, but will now observe, that the small round spot, which is
generally called the sight of the eye, is properly denominated the
_pupil_; and that the _retina_, is an expansion of the optic nerve on
the back part of the ball of the eye, upon which, as upon a screen, the
rays fall, which enter at the pupil. The rays of light, enter at the
pupil of the eye, and proceed to the retina; and there they describe the
figure, colour, and (excepting size) form a perfect representation of
the object, from which they proceed. We shall again close the shutters,
and admit the light, through the small hole made for that purpose, and
you will see a picture, on the wall, opposite the aperture, similar to
that which is delineated on the retina of the eye. The picture is
somewhat confused, but by using a lens, to bring the rays to a focus, it
will be rendered very distinct.
_Caroline._ Oh, how wonderful! There is an exact picture in miniature of
the garden, the gardener at work, the trees blown about by the wind. The
landscape, would be perfect, if it were not reversed; the ground, being
above, and the sky beneath.
_Mrs. B._ It is not enough to admire, you must understand, this
phenomenon, which is called a _camera obscura_, or dark chamber; from
the necessity of darkening the room, in order to exhibit it. The camera
obscura, sometimes consists of a small box, properly fitted up, to
represent external objects.
This picture, you now see, is produced by the rays of light, reflected
from the various objects in the garden, and which are admitted through
the hole in the window shutter.
[Illustration: PLATE XVI.]
The rays from the glittering weathercock, at the top of the alcove, A,
(plate 16.) represent it in this spot, _a_; for the weathercock, being
much higher than the aperture in the shutter, only a few of the rays,
which are reflected by it, in an obliquely descending direction, can
find entrance there. The rays of light, you know, always move in
straight lines; those, therefore, which enter the room, in a descending
direction, will continue their course in the same direction, and will
consequently fall upon the lower part of the wall opposite the aperture,
and represent the weathercock, reversed in that spot, instead of erect,
in the uppermost part of the landscape.
_Emily._ And the rays of light, from the steps, (B) of the alcove, in
entering the aperture, ascend, and will describe those steps in the
highest, instead of the lowest, part of the landscape.
_Mrs. B._ Observe, too, that the rays coming from the alcove, which is
to our left, describe it on the wall, to the right; while those, which
are reflected by the walnut tree, C D, to our right, delineate its
figure in the picture, to the left, _c d_. Thus the rays, coming in
different directions, and proceeding always in right lines, cross each
other at their entrance through the aperture; those which come from
above, proceed below, those from the right, go to the left, those from
the left, towards the right; thus every object is represented in the
picture, as occupying a situation, the very reverse of that which it
does in nature.
_Caroline._ Excepting the flower-pot, E F, which, though its position is
reversed, has not changed its situation in the landscape.
_Mrs. B._ The flower-pot, is directly in front of the aperture; so that
its rays, fall perpendicularly upon it, and consequently proceed
perpendicularly to the wall, where they delineate the object, directly
behind the aperture.
_Emily._ And is it thus, that the picture of objects, is painted on the
retina of the eye?
_Mrs. B._ Precisely. The pupil of the eye, through which the rays of
light enter, represents the aperture in the window-shutter; and the
image, delineated on the retina, is exactly similar to the picture on
the wall.
_Caroline._ You do not mean to say, that we see only the representation
of the object, which is painted on the retina, and not the object
itself?
_Mrs. B._ If, by sight, you understand that sense, by which the presence
of objects is perceived by the mind, through the means of the eyes, we
certainly see only the image of those objects, painted on the retina.
_Caroline._ This appears to me quite incredible.
_Mrs. B._ The nerves, are the only part of our frame, capable of
sensation: they appear, therefore, to be the instruments, which the mind
employs in its perceptions; for a sensation, always conveys an idea, to
the mind. Now it is known, that our nerves can be affected only by
contact; and for this reason, the organs of sense, cannot act at a
distance: for instance, we are capable of smelling only particles which
are actually in contact with the nerves of the nose. We have already
observed, that the odour of a flower consists in effluvia, composed of
very minute particles, which penetrate the nostrils, and strike upon the
olfactory nerves, which instantly convey the idea of odour to the mind.
_Emily._ And sound, though it is said to be heard at a distance, is, in
fact, heard only when the vibrations of the air, which convey it to our
ears, strike upon the auditory nerve.
_Caroline._ There is no explanation required, to prove that the senses
of feeling and of tasting, are excited only by contact.
_Mrs. B._ And I hope to convince you, that the sense of sight, is so
likewise. The nerves, which constitute the sense of sight, are not
different in their nature from those of the other organs; they are
merely instruments which convey ideas to the mind, and can be affected
only on contact. Now, since real objects cannot be brought to touch the
optic nerve, the image of them is conveyed thither by the rays of light,
proceeding from real objects, which actually strike upon the optic
nerve, and form that image which the mind perceives.
_Caroline._ While I listen to your reasoning, I feel convinced; but when
I look upon the objects around, and think that I do not see them, but
merely their image painted in my eyes, my belief is again staggered. I
cannot reconcile to myself, the idea, that I do not really see this book
which I hold in my hand, nor the words which I read in it.
_Mrs. B._ Did it ever occur to you as extraordinary, that you never
beheld your own face?
_Caroline._ No; because I so frequently see an exact representation of
it in the looking-glass.
_Mrs. B._ You see a far more exact representation of objects on the
retina of your eye: it is a much more perfect mirror, than any made by
art.
_Emily._ But is it possible, that the extensive landscape, which I now
behold from the window, should be represented on so small a space, as
the retina of the eye?
_Mrs. B._ It would be impossible for art to paint so small and distinct
a miniature; but nature works with a surer hand, and a more delicate
pencil. That power alone, which forms the feathers of the butterfly, and
the organs of the minutest insect, can pourtray so admirable and
perfect a miniature, as that which is represented on the retina of the
eye.
_Caroline._ But, Mrs. B., if we see only the image of objects, why do we
not see them reversed, as you showed us they were, in the camera
obscura? Is not that a strong argument against your theory?
_Mrs. B._ Not an unanswerable one, I hope. The image on the retina, it
is true, is reversed, like that in the camera obscura; as the rays, from
the different parts of the landscape, intersect each other on entering
the pupil, in the same manner as they do, on entering the camera
obscura. The scene, however, does not excite the idea of being inverted,
because we always see an object in the direction of the rays which it
sends to us.
_Emily._ I confess I do not understand that.
_Mrs. B._ It is, I think, a difficult point to explain clearly. A ray
which comes from the upper part of an object, describes the image on the
lower part of the retina; but, experience having taught us, that the
direction of that ray is from above, we consider that part of the object
it represents as uppermost. The rays proceeding from the lower part of
an object, fall upon the upper part of the retina; but as we know their
direction to be from below, we see that part of the object they describe
as the lowest.
_Caroline._ When I want to see an object above me, I look up; when an
object below me, I look down. Does not this prove that I see the objects
themselves? for if I beheld only the image, there would be no necessity
for looking up or down, according as the object was higher or lower,
than myself.
_Mrs. B._ I beg your pardon. When you look up, to an elevated object, it
is in order that the rays reflected from it, should fall upon the retina
of your eyes; but the very circumstance of directing your eyes upwards,
convinces you that the object is elevated, and teaches you to consider
as uppermost, the image it forms on the retina, though it is, in fact,
represented in the lowest part of it. When you look down upon an object,
you draw your conclusion from a similar reasoning; it is thus that we
see all objects in the direction of the rays which reach our eyes.
But I have a further proof in favour of what I have advanced, which, I
hope, will remove your remaining doubts: I shall, however, defer it till
our next meeting, as the lesson has been sufficiently long to-day.
Questions
1. (Pg. 157) What is optics?
2. (Pg. 157) What is meant by a luminous body?
3. (Pg. 157) What is meant by a dark body, and what by an opaque body?
4. (Pg. 157) What are transparent bodies?
5. (Pg. 157) What is a medium?
6. (Pg. 158) How is light projected from luminous bodies, and how, from
every point of such bodies, (fig. 1, plate 15?)
7. (Pg. 158) Why do not the rays of light from different points, stop
each other's progress?
8. (Pg. 158) What is a ray, and what a pencil of rays? fig. 2, plate 15.
9. (Pg. 158) Do we know whether light is a substance, similar to bodies
in general?
10. (Pg. 158) When a ray of light falls upon an opaque body, what is the
result?
11. (Pg. 159) In what does shadow consist?
12. (Pg. 159) Why are they, in general, but partially dark?
13. (Pg. 159) Upon what does the intensity of a shadow depend?
14. (Pg. 159) How are shadows affected by the size of the luminous body,
as represented in plate 15, fig. 3?
15. (Pg. 159) When is the shadow larger than the intercepting body?
16. (Pg. 160) What is explained by fig. 4, plate 15?
17. (Pg. 160) What will be the effect of several lights, as in fig. 5,
plate 15?
18. (Pg. 160) Why will neither of these shadows be very dark?
19. (Pg. 160) What becomes of the light which falls upon an opaque body?
20. (Pg. 160) What is meant by reflection?
21. (Pg. 161) What is meant by the incident, and reflected rays?
22. (Pg. 161) What is the result, when the incident ray falls
perpendicularly, and what, when it falls obliquely?
23. (Pg. 161) What two angles are always equal in this case?
24. (Pg. 161) To what law in mechanics, is this analogous, as
represented in fig. 4, plate 2?
25. (Pg. 161) What is represented by fig. 6, plate 15?
26. (Pg. 161) By what light are we enabled to see opaque, and by what,
luminous bodies?
27. (Pg. 161) What enables us to see a ray of light in its passage,
through a darkened room?
28. (Pg. 162) By what reasoning would you prove that an object, such,
for example, as a house, is seen by reflected light?
29. (Pg. 162) Why may one side of such object appear more bright than
another side?
30. (Pg. 162) How is the fact exemplified by the sun, or moon, shining
upon water?
31. (Pg. 162) Why is this best evinced by moonlight?
32. (Pg. 163) By what light do we see the moon, and why is it
comparatively feeble?
33. (Pg. 163) What circumstance, renders objects seen by moonlight,
still less vivid?
34. (Pg. 164) What is meant by the pupil of the eye?
35. (Pg. 164) What by the retina?
36. (Pg. 164) How do the rays of light operate on the eye in producing
vision?
37. (Pg. 164) How may this be exemplified, in a darkened room?
38. (Pg. 164) What is meant by a _camera obscura_?
39. (Pg. 164) How is it explained in plate 16?
40. (Pg. 165) Why are the objects inverted and reversed?
41. (Pg. 165) What analogy is there between the camera obscura, and the
eye?
42. (Pg. 165) Is it the object, or its picture on the retina, which
presents to the mind an idea of the object seen?
43. (Pg. 166) By what organs is sensation produced, and how must these
organs be affected?
44. (Pg. 166) How will the idea of contact, apply to objects not
touching the eye?
45. (Pg. 167) Why do not objects appear reversed to the eye, as in the
camera obscura?
CONVERSATION XV.
OPTICS--_continued_.
ON THE ANGLE OF VISION, AND THE REFLECTION OF MIRRORS.
ANGLE OF VISION. REFLECTION OF PLAIN MIRRORS. REFLECTION OF CONVEX
MIRRORS. REFLECTION OF CONCAVE MIRRORS.
CAROLINE.
Well, Mrs. B., I am very impatient to hear what further proofs you have
to offer, in support of your theory. You must allow, that it was rather
provoking to dismiss us as you did at our last meeting.
_Mrs. B._ You press so hard upon me with your objections, that you must
give me time to recruit my forces.
Can you tell me, Caroline, why objects at a distance, appear smaller
than they really are?
_Caroline._ I know no other reason than their distance.
_Mrs. B._ It is a fact, that distance causes objects to appear smaller,
but to state the fact, is not to give the reason. We must refer again to
the camera obscura, to account for this circumstance; and you will find,
that the different apparent dimensions of objects at different
distances, proceed from our seeing, not the objects themselves, but
merely their image on the retina. Fig. 1, plate 17, represents a row of
trees, as viewed in the camera obscura. I have expressed the direction
of the rays, from the objects to the image, by lines. Now, observe, the
ray which comes from the top of the nearest tree, and that which comes
from the foot of the same tree, meet at the aperture, forming an angle
of about twenty-five degrees; the angle under which we see any object,
is called, the visual angle, or, angle of vision. These rays cross each
other at the aperture, forming equal angles on each side of it, and
represent the tree inverted in the camera obscura. The degrees of the
image, are considerably smaller than those of the object, but the
proportions are perfectly preserved.
[Illustration: PLATE XVII.]
Now, let us notice the upper and lower ray, from the most distant tree;
they form an angle of not more than twelve or fifteen degrees, and an
image of proportional dimensions. Thus, two objects of the same size, as
the two trees of the avenue, form figures of different sizes in the
camera obscura, according to their distance; or, in other words,
according to the angle of vision under which they are seen. Do you
understand this?
_Caroline._ Perfectly.
_Mrs. B._ Then you have only to suppose, that the representation in the
camera obscura, is similar to that on the retina.
Now, since objects of the same magnitudes, appear to be of different
dimensions, when at different distances from us, let me ask you which it
is, that you see; the real objects, which, we know, do not vary in size,
or the images, which, we know, do vary, according to the angle of vision
under which we see them?
_Caroline._ I must confess, that reason is in favour of the latter. But
does that chair, at the further end of the room, form an image on my
retina, much smaller than this which is close to me? they appear exactly
of the same size.
_Mrs. B._ Our senses are imperfect, but the experience we acquire by the
sense of touch, corrects the illusions of our sight, with regard to
objects within our reach. You are so perfectly convinced, of the real
size of objects, which you can handle, that you do not attend to the
apparent difference.
Does that house appear to you much smaller, than when you are close to
it?
_Caroline._ No, because it is very near us.
_Mrs. B._ And yet you can see the whole of it, through one of the
windows of this room. The image of the house on your retina must,
therefore, be smaller than that of the window through which you see it.
It is your knowledge of the real magnitude of the house which prevents
your attending to its apparent size. If you were accustomed to draw from
nature, you would be fully aware of this difference.
_Emily._ And pray, what is the reason that, when we look up an avenue,
the trees not only appear smaller as they are more distant, but seem
gradually to approach each other, till they meet in a point?
_Mrs. B._ Not only the trees, but the road which separates the two rows,
forms a smaller visual angle, in proportion as it is more distant from
us; therefore, the width of the road gradually diminishes, as well as
the size of the trees, till at length the road apparently terminates in
a point, at which the trees seem to meet.
_Emily._ I am very glad to understand this, for I have lately begun to
learn perspective, which appeared to me a very dry study; but now that I
am acquainted with some of the principles on which it is founded, I
shall find it much more interesting.
_Caroline._ In drawing a view from nature, it seems that we do not copy
the real objects, but the image they form on the retina of our eyes?
_Mrs. B._ Certainly. In sculpture, we copy nature as she really exists;
in painting, we represent her, as she appears to us.
We must now conclude the observations that remain to be made, on the
angle of vision.
If the rays, proceeding from the extremities of an object, with an
ordinary degree of illumination, do not enter the eye under an angle of
more than two seconds, which is the 1-1800th part of a degree, it is
invisible. There are, consequently, two cases in which objects may be
invisible; if they are either so small, or so distant, as to form an
angle of less than two seconds of a degree.
In like manner, if the velocity of a body does not exceed 20 degrees in
an hour, its motion is imperceptible.
_Caroline._ A very rapid motion may then be imperceptible, provided the
distance of the moving body, is sufficiently great.
_Mrs. B._ Undoubtedly; for the greater its distance, the smaller will be
the angle, under which its motion will appear to the eye. It is for this
reason, that the motion of the celestial bodies is invisible, although
inconceivably rapid.
_Emily._ I am surprised, that so great a velocity as 20 degrees an hour,
should be invisible.
_Mrs. B._ The real velocity depends upon the space comprehended in each
degree, and upon the time, in which the moving body, passes over that
space. But we can only know the extent of this space, by knowing the
distance of the moving body, from its centre of motion; for supposing
two men to set off at the same moment from A and B, (fig. 2.) to walk
each to the end of their respective lines, C and D; if they perform
their walk in the same space of time, they must have proceeded at a
very different rate; and yet to an eye situated at E, they will appear
to have moved with equal velocity, because they will both have gone
through an equal number of degrees, though over a very unequal length of
ground. The number of degrees over which a body moves in a given time,
is called its angular velocity; two bodies, you see, may have the same
angular, or apparent velocity, whilst their real velocities may differ
almost infinitely. Sight is an extremely useful sense, no doubt, but it
cannot always be relied on, it deceives us both in regard to the size
and the distance of objects; indeed, our senses would be very liable to
lead us into error, if experience did not set us right.
_Emily._ Between the two, I think that we contrive to acquire a
tolerably accurate idea of objects.
_Mrs. B._ At least sufficiently so, for the general purposes of life. To
convince you how requisite experience is, to correct the errors of
sight, I shall relate to you, the case of a young man, who was blind
from his infancy, and who recovered his sight at the age of fourteen, by
the operation of couching. At first, he had no idea, either of the size,
or distance of objects, but imagined that every thing he saw touched his
eyes; and it was not, till after having repeatedly felt them, and walked
from one object to another, that he acquired an idea of their respective
dimensions, their relative situations, and their distances.
_Caroline._ The idea that objects touched his eyes, is, however, not so
absurd, as it at first appears; for if we consider that we see only the
image of objects, this image actually touches our eyes.
_Mrs. B._ That is, doubtless, the reason of the opinion he formed,
before the sense of touch had corrected his judgment.
_Caroline._ But since an image must be formed on the retina of each of
our eyes, why do we not see objects double?
_Mrs. B._ The action of the rays, on the optic nerve of each eye, is so
perfectly similar, that they produce but a single sensation; the mind,
therefore, receives the same idea, from the retina of both eyes, and
conceives the object to be single.
_Caroline._ This is difficult to comprehend, and I should think, can be
but conjectural.
_Mrs. B._ I can easily convince you, that you have a distinct image of
an object formed on the retina of each eye. Look through the window,
with both eyes open, at some object exactly opposite to one of the
upright bars of the sash.
_Caroline._ I now see a tree, the body of which, appears to be in a line
exactly opposite to one of the bars.
_Mrs. B._ If you now shut your right eye, and look with the left, it
will appear to the left of the bar; then by closing the left eye, and
looking with the other, it will appear to the right of the bar.
_Caroline._ That is true, indeed!