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The following are the colours of the rings, observed by reflection and transmission, commencing from the centre or point of apparent contact, as given by Sir Isaac Newton.* The curved line ca represents the section of one half the convex lens, and the straight one CB that of half the plane glass against which it is pressed.

499. The following are the thicknesses, expressed in millionth parts of inches, of plates of air, water, and glass, required to produce the different coloured rings:

Optice. Lib. ii., pars. 2.

By aid of this table, the thickness of thin films of air, water, or glass, may be readily determined by observing the colours they reflect. The comparative thickness of plates of two substances, reflecting the same colour, are in the inverse ratio of their indices of refraction (445).

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500. When these rings are observed by homogeneous light, they present the same hue as that of the light itself; alternating with dark and almost non-luminous rings, they appear to possess the greatest breadth in red, and the least in violet light. These rings appear to be larger, in proportion as we look at them in a more oblique direction; this is best seen by examining the rings produced, when a glass prism is pressed on the surface of a convex lens.

The coloured rings thus exhibited by thin plates, are produced by the interference of the light reflected by the first surface with that reflected from the second (431*); for when either of these reflected rays is intercepted, the colours entirely vanish.

501. The rings seen by transmission, are produced by those undulations which are not reflected, and are consequently propagated through the thickness of both glasses. Those luminous rays, which, when combined with the reflected rays, produced white light, being propagated through the glass, produce the transmitted or complementary (498) rings.

From Newton's table (499), we see that air, at or below a thickness of half a millionth of an inch, and water and glass at a thickness of about one third of a millionth of an inch, cease to reflect light, and appear, consequently, black. Films and fibres of quartz, so minute as not to be capable of propagating luminous undulations, have been met with and described by Sir David Brewster.

502. It is by no means necessary that very thin plates should be used to exhibit colours, for plates of any thickness, so arranged as to cause the interference of luminous undulations, will produce the same effect. This may be shown by fixing two slips of plate glass, about 0.10 inch distant from

* These rings may be exhibited by merely placing two plates of window glass, about four inches square, together, and passing them in the centre by means of a pointed piece of metal. The different coloured rings, somewhat eccentrically arranged, will appear with great beauty around the point where the pressure is applied.

each other, by means of two pieces of wax, and then by pressing one end of each plate together, they may be so fixed as to describe a very acute angle with each other. On looking at a candle, through that part of the plates nearest each other, numerous reflected images of it will become visible; the first of them appears crossed by a series of beautiful bands or fringes. These increase in breadth by diminishing the inclination of the plates; they are produced by the interference of the waves of light reflected from both surfaces of each glass plate.

503. The coloured rings, observed by regarding the sun, or other luminous body, through a piece of glass, covered with minute particles, as of dust, lycopodium, &c., or of water, by breathing on it, are all owing to the interference of luminous undulations inflected round the particles (490). A similar explanation will apply to the colours seen, by scattering fine powders or dust on, or before a mirror exposed to the solar rays. The beautiful tints presented by mother of pearl, and other natural or artificial substances, whose surface are marked by minute striæ, are all explicable on the hypothesis of interference; all that is requisite to produce these colours being, that the depression shall be of such a depth, as to cause an alteration in the path of rays incident upon them, equal to a fraction of the length of an undulation (486).

504. Among the natural phenomena which serve to illustrate the laws and principles laid down in this and the preceding chapters, the well-knownrain bow and less frequent mirage especially deserve attention. The former consists of a coloured arch, apparently suspended in the sky, and opposite to the sun, and is usually composed of two bows, termed primary and secondary, and sometimes even of other supplementary arches. The rainbow is never seen unless a shower of rain is falling, or the spray of water, as from a cataract, rising between the spectator and that portion of the sky opposite to the sun. To explain the cause of these bows, let FE be two drops of water, and ss solar rays incident upon

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S

each of them, those which enter near their centre will be refracted to a focus, as in a sphere of glass (453). But those which enter near their upper part suffer refraction, during which the light becomes resolved into waves of different lengths, as in prismatic refraction (467), and colours are consequently produced; the violet ray being most, and the red least refracted, the other rays being arranged between them in the usual manner. As these refracted rays are incident at the back of the drop, within the limiting angle. (448), they are reflected, and emerge at the lower parts, as G in the drop E, and present to the eye of the spectator a bow of the prismatic colours, bounded above by the red, and below by the violet rays.

When the solar rays enter the drops of rain from below, as at GH, they are refracted to the back of the drop, and undergo the same resolution into coloured rays; thence are reflected to the top, and thence to the front of the drop, where they emerge, presenting to the spectator the appearance of a second bow, exterior to the first, and with its tints much fainter and reversed, in consequence of the rays having suffered two reflections in GH, whilst in FE they underwent but one.

505. If an object, situated at or near the horizon, be so far from us, that, in consequence of the curvature of the earth, a right line could not connect it with the eye of the spectator, it will be invisible, except under a few remarkable states, constituting the phenomena of unusual refraction. For the production of these effects, it is necessary that the