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No. 2, a plano-convex lens; No. 3, a double convex; No. 4, a plano-concave; No. 5, a double concave; No. 6, a meniscus; No. 7, a multiplying glass; and No. 8, a prism. The term lens is usually given to such glasses or substances only as either magnify or diminish. Nos. 2, 3, 4, and 5, are therefore lenses; No. 6 is also a lens when its surfaces are portions of different spheres; but when they are of equal radii, or parallel, it has only the effect of a plane glass. A ray entering the plane glass, No. 1, will ,be refracted; but it will undergo another refraction on its emergence, which will rectify the former; the place of the object will, therefore, be a little altered, but the figure will remain the same. Suppose A B, Fig. 1, to represent a solid piece of glass with two parallel surfaces, an incident ray E F will be refracted into F G, and F G will be refracted on passing from the second surface into G H, parallel to the original direction EF. If parallel rays enter the plano-convex glass, as shown by

Fig. 1.

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Fig. 2.

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Fig. 2, the ray E will be refracted upwards to F, and the ray K will be refracted downwards to the same point; there they will cross, and then go onward in a straight line, and continue to diverge till intercepted by some obstacle. When parallel rays fall upon a double convex glass, K G, they will be refracted still more abruptly, and meet sooner in a point or principal focus at F. The distance of this focus is equal to the semi-diameter of the circle which the convexity of the glass continued, would produce. Either this glass or the former, as they collect the rays of the sun into a point, will burn at that point, the whole force of the rays that pass through them being concentrated there.

From all luminous objects, the rays of light proceed in a state of divergence; but when the distance from which they come is very great, the quantity of divergence is too small to require notice. The fixed stars and the sun, for example, are so immensely distant, that their rays are always considered as parallel; and it is only parallel rays which are converged to a focus in the manner described. Divergent rays proceeding from a point, as the flame of a candle, will be differently affected. If, therefore, a candle be placed exactly at the focal distance of a single or double convex lens, the rays will emerge parallel to each other. If the candle be placed nearer to the glass than its focal distance, the rays, after passing through the glass, will no longer be parallel, but separate or diverge. If the candle be placed still further off, the rays will then strike the glass more nearly parallel, and will, therefore, upon passing through, converge or unite at a distance behind the glass, more nearly approaching the distance at which parallel rays would be converged. After the rays have united in a focus, they will cross each other, and form an inverted picture of the flame of a candle, which may be received on a piece of paper placed at the meeting of the rays behind.

The cause of the inversion of the image is evident, the upper rays being those which come from the under part of the luminous body; and the under rays, on the contrary, coming from the upper part.

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In looking through a plano-convex or double convex lens, the object appears magnified agreeably to the rule, that we see every thing in the direction of the lines in which the rays last approach the eye; consequently, the larger the angle under which an object is seen, the larger that object will appear. From lenses the reverse in form to those we have noticed, we naturally expect opposite effects; accordingly, the attractive and refractive powers of a plano-concave and double-concave lens are not towards the centre, but towards the circumference. Parallel rays falling upon these lenses diverge, or are dispersed Rays already divergent are rendered more so, and convergent rays are made less convergent; hence objects seen through one of these glasses appear smaller than to the naked eye. Let a b, in the subjoined figure, represent an arrow, which would be seen by the eye, if no lens were before it, by the convergent rays acbi; but if the double-concave glass D H be interposed between the object and the eye, the ray a c will be bent towards g, and the ray b i will be bent towards h, and consequently both will be useless, as they do not enter the eye.

The object, then, will be seen by the rays aobr, which, on entering the glass, will be refracted into the lines o c and r i; and, according to the rule laid down, the object will be seen in the last direction of these rays; therefore, as the angle ocr is so much smaller than the angle acb, the arrow necessarily appears diminished; and as, with the diminution of its apparent size, we connect the idea of its being further off, it seems to be at the distance n m.

The miniscus acts like a convex lens when it is thickest in' the middle, that is, when its convex surface is a portion of a less sphere than its concave one; on the contrary, when it is thinnest in the middle, or has its concave surface a portion of a less sphere than the other, it has the effect of a concave lens. The axis of a lens, is a line supposed to be drawn through the centre of its spherical surfaces. When one side of the lens is plane, the axis is perpendicular to that side. The axis of a lens continued, would pass exactly through the centre of that sphere, of which the lens is the segment. The focus of a plano-convex lens is at a distance from the convex surface equal to the diameter of the sphere of which it is a part; and that of a double and equally convex lens is at half the same distance. The distance of the focus of a solid globe or ball of glass is one quarter of its diameter from the nearest part of the ball. To explain the effect of the multiplying glass, (No. 7,) it will only be necessary to revert to the principle, that objects appear in the direction of the line last described by the rays that render them visible; hence, if the object B, (p 213.) is seen through the glass E H by the ray B A that passes through the surface F G, the object, by the eye at A, will be seen at B; the ray B G passes through the surface G H, and after refraction comes to the eye in the direction of A D, as it proceeded from D, and therefore the object appears at D; and for the same reason, through the surface F E, it appears at C; consequently, there will be the appearance of as many objects as there are flat surfaces on the glass, for each of them shows the same object in a different place.

The disposition of the rays of light to be turned back into the medium from whence they came, is called their reflexibility; the change of direction produced by their being actually turned back, is called reflection. All objects which are not themselves luminous are rendered visible by reflection; and glass, crystal, water, and the most pellucid media, reflect a portion of the rays of light which fall on them, or their forms and substance could not be distinguished. On the other hand, the whole of the incident light is not reflected from any surface, however bright, smooth, and opaque. It is calculated that the best mirrors reflect little more than half the light they receive; the part lost consists of two portions, one of which, and by far the largest, being absorbed by the mirror, and the other, scattered by irregular reflection. Light is always lost, in passing through the most transparent bodies, by the same laws.

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The different refrangibility of the rays of light is demonstrated by the prism. If a beam of light from the sun be let into a darkened room, and be received upon a white screen or opposite wall, it will form a circular image, and will be of one uniform whiteness. If a prism be interposed, so that the light must pass through it before it reaches the wall, the image is no longer circular or white; it assumes an oblong shape, terminated by semicircular arches, and exhibits seven different colours. This oblong image is called the spectrum. In the whole range of philosophical experiment, a more beautiful appearance cannot be presented to the eye, and instructive nature will appear not less extraordinary than its beauty, when it is considered, that the investigation of the cause of it led Sir Isaac Newton to form the first rational theory of the cause of colours. The seven colours of the spectrum are called the original, or primary colours. If a spectrum be divided into 100 parts, the red part of it is found to occupy 11 of these parts; the orange 8, the yellow 14, the green 17, the blue 17, the indigo 11, and the violet 22. The red part of the spectrum is nearest the prism; and the violet, at the greatest distance.

It is clear, from this, that light is not homogenous, because the attractive power of the prism is greater upon some parts of it than upon other parts. Accordingly, it is generally concluded that the solar beam or white light is composed of particles differing in size and density; that this difference of their size and density is the cause of their being differently refrangible; and that the separation of the rays of one or more sizes from the rest, by various means, produces all the diversity of colours which affect our sight. It is found, that the red part of light is capable of struggling through thick and resisting mediums, when all the other colours are stopped. Thus, the sun appears red when seen through a fog. The particles which compose orange light are next, in size and refrangibility, to the red; and so on to the violet, which consists of the smallest particles, and which are, therefore, the most turned out of their course. White is composed of all the primary colours, mixed together in their due proportions.

When bodies reflect the rays of light in the proportion in which they exist in the solar beam, they appear white; when they reflect none of the rays, they appear black.

Convex lenses in their simple state have been applied to collect the heat of the sun's rays, for purposes similar to those of burning mirrors. A burning lens must be convex; a burning mirror, concave; because both produce their effect by concentrating into a focus the rays of light and heat incident upon a large surface. As the rays which pass through a convex lens, or are reflected from a concave mirror, are united at its focus, their effect is so much the greater, as the surface of the lens or mirror exceeds that of the focus. Thus, if a lens four inches in diameter collect the sun's rays into a focus at the distance of one foot, the focal image will not be more than one-tenth of an inch broad. The surface of this circle is 1600 times less than the surface of the lens, consequently the density of the sun's rays within it is proportionately increased. It has been found, that large lenses and mirrors burn with irresistible intensity when properly constructed, dispersing the hardest metals and other substances into gas, often in a few seconds.

See Burning Glass, and the various other optical instruments, under their respective names.