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of the object, the area of the lens, nor its focal distance is given, the brightness of the image will be directly as the area of the lens, and inversely as the squares of the distances of the object and image conjointly. B= L

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Now as the distance of the object is always inversely as the distance of the image, the one approaching the lens, while the other recedes from it, the brightness of the image will solely depend upon the area of the lens, and will not be altered by the alteration of the distance

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The brightness of an image will always be proportional to the brightness of the object, when all other circumstances are equal. Hence the brightness of the solar image, in the focus of a burning glass, is so much greater than that of any other object.

The heat at the focus of a burning glass is always directly as the area of the glass, and inversely as the area of the solar image, or the square of its focal length. For as the area of the glass is larger, so many more rays are transmitted through it, and the smaller the space is, into which they are condensed at the focus, the more intense will be the heat, which will be to the common heat of the sun, as the area of the glass is to the area of the solar image. For the common heat of the sun is the heat of the rays when they are spread over the surface of the glass; and the same rays being collected into the area of the solar image will produce a brightness and heat proportional to the smallness of the space into which they are condensed.

VISION THROUGH LENSES.

WHEN any small object or point of an object is seen by a ray of light refracted through a lens, it appears in the direction in which the refracted ray comes to the eye, and in that place from whence the rays seem to diverge, or their radiant point.

Every pencil of rays, that diverges from any point of an object, will by passing through a lens have the direction of its rays altered, as if they came from some other point in the axis of the pencil, more or less distant than the object; which is called the radiant point of that pencil; and as the eye is not sensible of this change of direction in the rays, we naturally refer the point of the object from whence they proceed, to this radiant point; as the image is painted on the same part of the eye, that it would have been painted on, had there been no lens, and the object was placed in the radiant point. Now, as there are as many imaginary radiants, as there are points in the object, the sum total of these constitutes what is called the last image. And as the eye is affected by this last image, or sum total of radiants, in the same manner as if the object had been seen without the lens, in the same place, and of the same magnitude with that image, we say, that it is not the object that we see by refracted vision, but its last image. Now this is universal in refracted vision, and all the various situations, positions, magnitudes, and appearances of objects seen by refracted rays, depend upon the different directions of the rays when they fall upon the eye, and the position of the radiant points, from which they seem to diverge; some of which we shall mention and illustrate.

In vision through any glass, the object will appear

erect, if both the object and its last image be on the same side of the lens, but inverted, if they be on different sides. If the object be placed nearer to a convex lens than its principal focus, the rays that diverge from it are rendered less diverging, as if they had come from a radiant point more distant than the object, and consequently the last image will be on the same side of the lens with the object: and as the middle ray, or axis of every pencil that proceeds from any point of an object, passes through the center of the lens without refraction, the other rays of that pencil will proceed diverging after refraction as if they had diverged from some point in the axis of the pencil more distant than the object: so that every point of the object will have its correspondent radiant situate somewhere in the line which passes from that point of the object through the center of the lens, and therefore the points of the image, consisting of all these radiants, must have the same position with respect to each other as the correspondent points of the object have, and the object will appear erect, when they are both on the same side of the lens.

As the rays that pass through a concave lens, converging to a point more distant than the principal focus, are made to diverge, and diverging rays to diverge more, as if they came from a point between the object and lens; the same reasoning proves that the last image, or all the radiant points, will be on the same side with the object, and that it will appear erect. In both these cases, the object and last image being seen from the center of the lens under the same angle, they must be to each other as their respective distances from the lens; the object appearing magnified by the convex lens, and diminished by the concave.

But if the object be placed beyond the principal fo

cus, the rays that proceed from it diverging, will be made to converge by a convex lens to a focus on the opposite side of the lens, where they form a distinct image; and the rays which are converged to the different points of this image will there cross each other and diverge from thence.

Now, if the eye be placed farther off, these intersecting rays will fall upon it diverging from the distinct picture; so that the last image and distinct picture will be in the same place; for every focal point of the one becomes a radiant point of the other. Hence the object will appear inverted, as the distinct image is inverted.

In this case also, the object and its last image will be to each other as their distances from the lens. This we before proved with respect to the object and distinct picture formed in the focus of the lens, and this distinct picture becomes the last image.

As the object and last image appear under the same angle from the center of the lens, if the eye be close to the lens, they will appear under the same angle, and consequently be of the same apparent diameter. This would also be the case if the lens were close to the object. Because the real and imaginary radiants then become the same; the object and last image being in the same place.

If the object be nearer to the convex lens than the principal focus, it will not only appear erect, but also brighter than to the naked eye, and distinct. It will appear brighter, because the rays diverge less after refraction, and more of them will consequently enter the eye; and as they diverge as if they had come from an object at a moderate distance, the object will appear as distinct as objects at a small distance generally appear. It will also appear magnified, unless either the object

or eye touch the lens, because the last image is more distant than the object, and both are viewed under the same angle from the center of the lens. But the apparent magnitude will continually decrease as the eye recedes from the lens, because the last image is always seen under a less angle as the eye recedes.

If the object be placed in the principal focus of the convex lens, the rays will proceed parallel after refrac tion, and therefore more of them will enter the eye than could have entered without the lens, and make the ob ject appear brighter, than to the naked eye. It will appear as distinct as remote objects usually appear, as the rays from them come nearly parallel. It will also appear erect, as the imaginary radiant points are at an infinite distance on the same side with the object. For the same reason, its apparent magnitude will not be altered by the motion of the eye, as no motion of the eye can lessen or increase this infinite distance of the radiant points. It will therefore appear of the same size, whether the eye be close to the lens, or removed from it. But as all objects appear to the naked eye to grow less, when the eye removes from them, and this not taking place when they are viewed through a convex lens, but that they still continue to appear of the same magnitude, upon any removal of the eye; we say, that the object will appear to be magnified, when the eye is removed from the lens, because it could not appear to the naked eye so large, as it appears at the increased distance of the eye, when seen through the lens.

If the object be farther from the lens than the principal focus, and the eye nearer than the place of the distinct picture, the object will appear erect, because the last image is still on the same side of the lens with the object; brighter than to the naked eye, because, as the

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