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 circ.u.mstance; 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.

[Ill.u.s.tration: 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 s.p.a.ce comprehended in each degree, and upon the time, in which the moving body, pa.s.ses over that s.p.a.ce. But we can only know the extent of this s.p.a.ce, 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 s.p.a.ce 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!

_Mrs. B._ There are, evidently, two representations of the tree in different situations, which must be owing to an image of it being formed on each eye; if the action of the rays, therefore, on each retina, were not so perfectly similar as to produce but one sensation, we should see double; and we find that to be the case with some persons, who are afflicted with a disease in one eye, which prevents the rays of light from affecting it in the same manner as the other.

_Emily._ Pray, Mrs. B., when we see the image of an object in a looking-gla.s.s, why is it not inverted, as in the camera obscura, and on the retina of the eye?

_Mrs. B._ Because the rays do not enter the mirror by a small aperture, and cross each other, as they do at the orifice of a camera obscura, or the pupil of the eye.

When you view yourself in a mirror, the rays from your eyes fall perpendicularly upon it, and are reflected in the same line; the image is, therefore, described behind the gla.s.s, and is situated in the same manner as the object before it.

_Emily._ Yes, I see that it is; but the looking-gla.s.s is not nearly so tall as I am, how is it, therefore, that I can see the whole of my figure in it?

_Mrs. B._ It is not necessary that the mirror should be more than half your height, in order that you may see the whole of your person in it, (fig. 3.) The ray of light A B, from your eye, which falls perpendicularly on the mirror B D, will be reflected back, in the same line; but the ray from your feet, will fall obliquely on the mirror, for it must ascend in order to reach it; it will, therefore, be reflected in the line A D: and since we view objects in the direction of the reflected rays, which reach the eye, and since the image appears at the same distance, behind the mirror, that the object is before it, we must continue the line A D to E, and the line C D to F, at the termination of which, the image will be represented.

[Ill.u.s.tration: PLATE XVIII.]