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the prolongation of the same rays coincide, and where there is formed for the eye the virtual image of the point a. For the same reason the eye sees at B the image of b; hence the image of AB appears at ab, but it is virtual; that is to say, it does not really exist, it could not be received on a screen, and is only an optical illusion.

It is to be remarked that in opposition to what takes place when

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the image is real, the virtual image is erect, and in all cases larger than the object; the rectification of the image arises from the fact, that the secondary axes do not intersect between the image and the object, but beyond it; the magnification arises from the image being further than the object from the point of intersection of the secondary axes which pass through a and b.

The term lens is applied to the lenticular glasses used as magnifying glasses. Everyone is aware, that if the print of a book be closely looked at through such a lens it will appear larger ; if the lens be progressively removed, a moment is reached when the characters disappear. This is the case when they are in the principal focus : when it is still further removed the characters reappear ; but they are reversed, for then they are beyond the principal focus.

330. Double concavelenses; foci and images.—We have seen, in speaking about double convex lenses, that as the thickness decreases from the centre towards the edges, the small plane facettes, corresponding to the incidence and convergence of the same ray, are more and more inclined from the centre to the periphery.

But in double concave lenses, on the contrary, where the thickness increases from the centre to the edge, the small facettes are more

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and more apart ; and hence the opposite phenomena. For, while double convex lenses cause the rays traversing them to coincide, by breaking them twice in the same direction, so as to bring them nearer the principal axis, double concave lenses produce the opposite effect, and only increase the divergence of the rays.

This phenomenon may be readily understood by reference to

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fig. 253, in which it is apparent how the rays are twice broken in the same direction, so as to diverge from the axis, and give rise to the diverging pencil MN. But the eye which receives this pencil is acted upon by it, as if the luminous object were at l; there is thus produced a virtual focus, the only one possible in double concave lenses.

As these kinds of lenses have only virtual foci, they can produce none but virtual images; these images are moreover always erect and smaller than the object. Thus let AB be an object seen through a double concave lens (fig. 254); the luminous pencil from A is deflected on passing through the lens in such a manner as to reach the eye as if it were emitted from a point, a, on the secondary axis, AO. In like manner, the pencil from the point, B, reaches the eye as if it started from the point, b. There is formed therefore at ab, between the secondary axes, AO and BO, a virtual image of the object, AB, which is smaller and erect. This image is necessarily always smaller than the object, for it is nearer the point, O, where the secondary axes intersect.

APPLICATION OF LENSES. 331. Refraction of heat.—When a pencil of solar light is received on a condensing lens, not merely is light concentrated on its focus, but heat also ; for if a piece of an inflammable substance, such as amadou, paper, cloth, wood, be placed in the focus, th


Fig. 255. body soon begins to burn. With lenses of large diameter metals even may be melted.

This property which condensing lenses have is utilised for producing fire in what are called burning glasses. They may be a source of danger, by becoming a source of fire, when a lens is exposed to the solar rays. The same accident may be produced by spherical glass vessels ; for they refract the light and heat like double convex lenses.

The concentration of the heat rays of the sun has received an application in certain solar dials, when the hour of midday is marked by the discharge of a small cannon (fig. 255). Above the cannon is a condensing lens, the focus of which exactly corresponds, to the touch-hole of the cannon the moment the sun passes the meridian of this place. Hence, the cannon being charged and primed beforehand, the lens ignites the powder just at midday, and the explosion announces the time at a distance.

Yet the time thus given is what is called in astronomy solar time, or true time, in which the length of day varies. Now our watches and clocks being regulated for mean time, that is to say, for an unchangeable day, only agree with the sun four times a year; December 24, April 15, June 15, and September 1. On February 11 a clock giving mean time is 14' 37" faster than the sun, and on November 3 it is 16' 17'' slow. The equation of time represents the amount which on all the days of the year must be added to or taken from the time of a clock to obtain the mean time. Hence it is incorrect to use the ordinary expression, that a good watch or a good clock goes like the sun.

332. Beacons. Lighthouses. These are fires lighted at night on high towers along the shores of the sea, in order to guide mariners in darkness and enable them to keep clear of danger.

Beacon fires were originally wood or coal fires ; but these were dull and unsteady. They were afterwards replaced by oil lamps placed in the principal focus of concave reflectors, which sent the reflected light to a great distance, for its rays were parallel.

In 1822 Fresnel made a great improvement in the illumination of lighthouses as they are now called. Abandoning the use of metallic reflectors, which soon tarnished under the influence of the sea-fogs, Fresnel substituted large plano-convex lenses, in the focus of which he placed a powerful lamp with four concentric wicks, and equal in illuminating power and quantity of oil consumed to seventeen Carcel lamps. But the difficulty of constructing such lenses, which must necessarily be large, and at the same time not thick, so as not to absorb much light, led Fresnel to

adopt a special system of lenses, known as echelon or lighthouse lenses.

Seen in front in fig. 256, and in profile in fig. 257, they consist of a plano-convex lens, A, a foot in diameter, 'round which are arranged eight or ten glass rings, which are also plano-convex, and whose curvature is calculated, so that each has the same focus as the central lens, A. A lamp being placed in the focus of this refracting system, an immense horizontal pencil, RC, is formed, which sends the light to a great distance. Further, above and below these lenses, are placed several silvered glass mirrors, mn.

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Thus the rays, which would be lost towards the sky and the earth, are utilised and sent in a horizontal direction. By this double combination a vast horizontal pencil is obtained, which sends the light of the lamp to a distance of 20 or 30 miles; but it only sends it in one direction. To increase the number of points of the horizon at which the light can be seen, Fresnel, instead of a single system of lenses and mirrors represented in fig. 257, united eight such arrangements, so as to form an enormous glass pyramid with eight faces, as seen in fig. 258, which represents a lighthouse lens of the largest size, constructed by M. Soutter, and exhibited at the

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