standard candle, it is scarcely possible to obtain an observing-room long enough for a direct comparison by any of the above methods. To overcome this difficulty a lens (either convex or concave), of short focal length, may be employed to form an image of the more powerful source near its principal focus. Then all the light which this source sends to the lens may be regarded as diverging from the image and filling a solid angle equal to that which the lens subtends at the image. In other words, the illuminations of the lens itself due to the source and the image are equal. Hence, if S and I are the distances of the source and image from the lens, the image is weaker than the source in the ratio of I2 to S2, and a direct comparison can be made between the light from the image and that from a standard candle. Thus, if a screen at distance D from the image has the same illumination from the image as from a candle D3 at distance C on the other side, the image is equal to a candles, and the source itself to candles. A correction must, however, be applied to this result for the light lost by reflection at the surfaces of the lens. D2 S2 CHAPTER LXVIII. REFLECTION OF LIGHT. 952. Reflection.-If a beam of the sun's rays AB (Fig. 659) be admitted through a small hole in the shutter of a dark room, and allowed to fall on a polished plane surface, it will be seen to continue its course in a different direction B C. This is an example of reflec tion. A B is called the incident beam, and BC the reflected beam. The angle ABD contained between an incident ray and the normal is called the angle of incidence; and the angle CBD contained between the corresponding reflected ray and the normal is called the angle of reflection. The plane ABD containing the incident ray and the normal is called the plane of incidence. 953. Laws of Reflection.-The reflection of light from polished surfaces takes place according to the following laws: 1. The reflected ray lies in the plane of incidence. 2. The angle of reflection is equal to the angle of incidence. These laws may be verified by means of the apparatus represented in Fig. 660. A vertical divided circle has a small polished plate of Reflection. fixed at its centre, at right angles to its plane, and two tubes travelling on its circumference with their axes always directed towards the centre. The zero of the divisions is the highest point of the circle, the plate being horizontal. A source of light, such as the flame of a candle, is placed so that its rays shine through one of the tubes upon the plate at the centre. As the tubes are blackened internally, no light passes through except in a direction almost Fig. 660.- Verification of Laws precisely parallel to the axis of the tube. The observer then looks through the other tube, and moves it along the circumference till he finds the position in which the reflected light is visible through it. On examining the graduations, it will be found that the two tubes are at the same distance from the zero point, on opposite sides. Hence the angles of incidence and reflection are equal. Moreover the plane of the circle is the plane of incidence, and this also contains the reflected rays. Both the laws are thus verified. 954. Artificial Horizon. These laws furnish the basis of a method of observation which is frequently employed for determining the altitude of a star, and which, by the consistency of its results, furnishes a very rigorous proof of the laws. A vertical divided circle (Fig. 661) is set in a vertical plane by proper adjustments. A telescope movable about the axis of the circle is pointed to a particular star, so that its line of collimation I'S' passes through the apparent place of the star. Another telescope, similarly mounted on the other side of the circle, is directed downwards along the line I'R towards the image of the star as seen in a trough of mercury I. Assuming the truth of the laws of reflection as above stated, the altitude of the star is half the angle between the directions of the two telescopes; for the ray SI from the star to the mercury is parallel to the line S'I', by reason of the excessively great distance of the star; and since the rays SI, IR are equally inclined to the normal IN, which is a vertical line, the lines I'S, I'R are also equally inclined to the vertical, or, what is the same thing, 1 In practice, a single telescope usually serves for both observations. are equally inclined to a horizontal plane. A reflecting surface of mercury thus used is called a mercury horizon, or an artificial horizon. Observations thus made give even more accurate results than those in which the natural horizon presented by the sea is made the standard of reference. 955. Irregular Reflection.-The reflection which we have thus far been discussing is called regular reflection. It is more marked as the reflecting surface is more highly polished, and (except in the case of metals) as the incidence is more oblique. But there is another kind of reflection, in virtue of which bodies, when illuminated, send out light in all directions, and thus become visible. This is called irregular reflection or diffusion. Regular reflection does not render the reflecting body visible, but exhibits images of surrounding objects. A perfectly reflecting mirror would be itself unseen, and actual mirrors are only visible in virtue of the small quantity of diffused light which they usually emit. The transformation of incident into diffused light is usually selective; so that, though the incident beam may be white, the diffused light is usually coloured. The power which a body possesses of making such selection constitutes its colour. The word reflection is often used by itself to denote what we have here called regular reflection, and we shall generally so employ it. 956. Mirrors. The mirrors of the ancients were of metal, usually of the compound now known as speculum-metal. Looking-glasses date from the twelfth century. They are plates of glass, coated at the back with an amalgam of quicksilver and tin, which forms the reflecting surface. This arrangement has the great advantage of excluding the air, and thus preventing oxidation. It is attended, however, with the disadvantage that the surface of the glass and the surface of the amalgam form two mirrors; and the superposition of the two sets of images produces a confusion which would be intolerable in delicate optical arrangements. The mirrors, or specula as they are called, of reflecting telescopes are usually made of speculum-metal, which is a bronze composed of about 32 parts of copper to 15 of tin. Lead, antimony, and arsenic are sometimes added. Of late years specula of glass coated in front with real silver have been extensively used; they are known as silvered specula. A coating of platinum has also been tried, but not with much success. The mirrors employed in optics are usually either plane or spherical. N M K T" Fig. 662.-Plane Mirror. N 957. Plane Mirrors.-By a plane mirror we mean any plane reflecting "surface. Its effect, as is well known, is to produce, behind the mirror,images exactly similar, both in form and size, to the real objects in front of it. This phenomenon is easily explained by the laws of reflection. Let M N (Fig. 662) be a plane mirror, and S a luminous point. Rays SI, SI', SI" proceeding from this point give rise to reflected rays IO, I′ O'′, I" O"; and each of these, if produced backwards, will meet the normal S K in a point S', which is at the same distance behind the mirror that S is in front of |