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situation in the landscape, for being immediately in front of the aperture, its rays fall perpendicularly upon it, and consequently proceed perpendicularly to the wall, where they delineate the object. It is thus that the picture of objects is painted on the retina of the eye. 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.
The different apparent dimensions of objects at different distances proceed from our seeing, not the objects themselves, but merely their image on the retina. Here is represented a row of trees, as viewed in the camera
obscura; the direction of the rays from the objects to the image is expressed by lines. Observe that 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; this is called the angle of vision, being that under which we see the tree. These rays cross each other at the aperture, and represent the tree inverted in the camera obscura. The dimensions of the image are considerably smaller than those of the object, but the proportions are perfectly preserved. The upper and lower ray, from the most distant tree, 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.
In sculpture we copy Nature as she really exists; in painting we represent her as she appears to us-that is to say, we do not copy the objects, but the image they form on the retina of the eye.
We cannot judge of the velocity of a body in motion unless we know its distance; for, supposing two men to set off at the same moment from A and B, 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.-Sight cannot be implicitly 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. Nothing more convincingly shows how requisite experience is to correct the errors of sight, than 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 everything he saw, touched his eyes; and it was not till after having repeatedly felt them, and walked from one object to another, that he required an idea of their respective dimensions, their relative situations, and their distances.
Since an image is formed on the retina of each of our eyes, it would seem that we ought to see objects double. In fact, however, we do not; and perhaps the best solution which has been offered of the difficulty is this, that 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. Persons afflicted with a disease in one eye, which prevents the rays of light froin affecting it in the same manner as the other, frequently see double.
The image of an object in a looking-glass is not in
verted, 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 a man views himself in a mirror, the rays from his eyes fall perpendicularly upon it, and are reflected in the same line; they proceed, therefore, as if they had come from a point behind the glass, and the same effect is produced as if they proceeded from an image of the object described behind the glass, and situated there in the same manner as the object before it. This is not the case only with respect to rays falling perpendicularly on the glass, but with all others. -Thus, a ray proceeding from the point c to D is reflected to A, and arrives there in the same manner as if it had proceeded from E, a point behind the glass, at the same distance from it as c is in front of it.
A man cannot see himself in a mirror if he stand to the right or to the left of it, because the incident rays falling obliquely on the mirror will be reflected obliquely in the opposite direction, the angles of incidence and reflection being equal.
There are three kinds of mirrors used in optics; the plane or flat, which are the common mirrors, convex mirrors, and concave mirrors. The reflection of the two latter is very different from that of the former.
The plane mirror, we have seen, does not alter the direction of the reflected rays, and forms an image behind the glass exactly similar to the object before it; for it forms an image of each point of the object at the same distance behind the mirror, that the point is before it; and these images of the different points together make up one image of the whole object. A convex mirror has the property of making the reflected rays diverge, by which means it diminishes the image; and a concave mirror makes the rays converge, and, under certain circumstances, magnifies the image. Let us begin by examining the reflection of a convex mirror.
This is formed of a portion of the exterior surface of a sphere. When several parallel rays fall upon it, that ray only which, if prolonged, would pass through the centre, or axis of the mirror, is perpendicular to it. In order to avoid confusion, we have drawn only three parallel lines, AB, CD, EF, to represent rays falling on the convex mirror, MN; the middle ray, you will observe, is perpendicular to the mirror, the others fall on it obliquely.— The three rays being parallel would all be perpendicular to a flat mirror; but no ray can fall perpendicularly on a spherical mirror, which
is not directed towards the centre of the sphere, just as a weight falls perpendicularly to the earth when gravity attracts it towards the centre. In order, therefore, that rays may fall perpendicularly to the mirror at в and F, the rays must be in the direction of the dotted lines which meet at the centre, o, of the sphere, of which the mirror forms a portion.
Now let us observe in what direction the three rays AB, CD, EF, will be reflected. The middle ray falling perpendicularly on the mirror will be reflected in the same line; the two others falling obliquely, will be reflected obliquely to G and H, for the dotted lines are perpendiculars, which divide their angles of incidence and reflection, or they will proceed as if they came from the point L; and since we see objects in the direction of the reflected ray, we shall see an image, answering to that which would be produced by a body placed at L, which is the point at which the reflected rays, if continued through the mirror, would unite and form an image. This point is equally distant from the surface and centre of the sphere, and is called the imaginary focus of the mirA focus is a point at which converging rays unite; in this case called an imaginary focus, because the rays
only appear to unite there, or rather proceed after reflection in the same direction as if they came from behind the mirror, from that point; for they do not pass through the mirror, since they are reflected by it.
A concave mirror is formed of a portion of the internal surface of a hollow sphere, and its peculiar property is to make the rays of light converge. If three parallel rays, A B, C D, E F, fall on the concave mirror, м N, the middle ray will be reflected in the same line, being in the direction of the axis of the mirror, and the two others will be reflected obliquely as they fall obliquely on the mirror. The two dotted perpendiculars divide their angles of incidence and reflection; and in order that these angles may be equal, the two oblique rays must be reflected to L, where they will unite with the middle ray. Thus when any number of parallel rays fall on a concave mirror, they are all reflected to a focus; for in proportion as the rays are more distant from the axis of the mirror, they fall more obliquely upon it, and are more obliquely reflected; in consequence of which they come to a focus in the direction of the axis of the mirror; and this point is not an imaginary focus, (as with the convex mirror,) but the true focus at which the rays unite. If rays fall convergent on a concave mirror, they are sooner brought to a focus, L, than parallel rays; their focus is therefore nearer to the mirror M N. Divergent rays are brought to a more distant focus than parallel rays,
where the focus is at L; but the true focus of mirrors, either convex or concave, is that formed by parallel rays, which is equally distant from the centre and the surface of the sphere. If a metallic concave mirror of polished tin
be exposed to the sun, the rays will
be collected into a very brilliant focus; and a piece paper held in this focus will take fire; for rays of