manner of the soap-film (Fig. 97). This method is within the power of many who like to construct their own apparatus.

It is clear that, knowing either the curve of the lens, or the thickness of the gold-leaf, it is very easy to calculate

the thickness of the film of air at any given distance from the centre. Newton found that when he employed pure monochromatic light, he obtained recurring rings of coloured light, or of darkness, as in A, B, C, D, E, F, Fig. 100, at once, twice, thrice, and other multiples of one definite small thickness. He soon discovered another beautiful fact, viz., that the rings

were broader, or required a thicker film, in red light than in blue light; and finally, by a movable prism, he threw the successive colours of the spectrum on the rings, and found them gradually contract as he travelled towards the violet end. With most lanterns there is hardly light enough to employ this beautiful method; but the phenomena may be shown as follows:-Arrange the Newton's rings, and focus on the screen as before. Provide one of the movable slide-frames now used by all lantern lecturers, and fit in it two half-size glasses, one blue and one red. Condense the full light on the rings; and as close to them as possible, between them and the nozzle, hold the slide; as it is moved from side to side, the rings will open or contract as the red or blue glass is interposed, and when they equally cover the rings, the two semi-circular segments will be seen not to coincide, the red being larger in diameter than the blue. It is easy to understand, therefore, why, if we employ white light, we must obtain rainbow-coloured circles.

100. Test of the Emission Theory.-Having to account for these phenomena, and adopting for practical purposes the Emission Theory (§ 58) as his working hypothesis,' Newton accounted for his bright and dark rings recurring at every multiple of a given thickness of the transparent film, by supposing that the "particles" of light suffer alternate "fits" of transmission or reflection, at regularly recurring intervals or distances. Professor Tyndall supposes that he imagined a rotation during their progressive motion, and this is not improbable; but it is only a supposition. If, then, light reaches the first surface of the film in a fit of transmission, it enters it and travels to the second surface; and if the thickness is such that it is in the same fit or phase

1 There is ample evidence in his Optics that Newton was very strongly attracted towards the Undulatory Theory, but did not feel justified in adopting it, owing to difficulties he was unable to solve.

when arrived at the second surface, it is again transmitted, and so is lost to view by reflected light. There is at that point, therefore, a dark ring; and obviously at every multiple of that thickness another dark ring. If, on the contrary, the particle is in the opposite or reflecting fit when it reaches the second surface, it is reflected and forms a bright ring.

or

"waves

It will be plain how, on either hypothesis, the "particles" " of red light are larger than those of blue. We can easily, however, test the two theories. Obviously all the light that has anything to do with the rings, according to the Emission Theory, enters the first surface; and the "fit" in which it reaches the second has alone anything to do with them. On our wave hypothesis, it is the interference of waves reflected from both surfaces that causes them. We have not come to Polarisation yet; but it may be briefly stated that polarised light utterly refuses to be reflected from glass at a certain angle; and this polarised light we readily obtain by fitting a "Nicol prism" on to the nozzle of our optical objective. All our light is then polarised; and when the long diameter is vertical and the Newton lenses are adjusted at an angle of 55° to 56° with the beam from the lantern, none of it will be reflected from the top glass, or in other words, from the first surface of the film. And when two plain glasses are used, none would be reflected from the second surface either. But metal is subject to quite other laws, and does reflect light copiously under such circumstances; therefore, by substituting for the bottom glass one which has been silvered or platinised, we can still get reflection from the second surface of the film of air. On Newton's theory, we ought therefore still to get the rings. But we do not. There is light on the screen, but the rings 1 For details and explanations on these points see Chaps. X. and XI. Only sufficient is stated here for the purposes of this experiment.

have vanished, in the proper position of the Nicol; to be restored again when this is so turned round as to restore reflection from the first surface also.

Further yet; if we next adjust the lenses so as to meet the light at a still greater angle (from the normal) than that of polarisation, and thus partially restore reflection from the first surface, on rotating the Nicol we get a complicated and beautiful phenomenon, first discovered by Arago; viz., in one position the rings are of certain colours, and when the Nicol is rotated 90° they show complementary colours. Detailed explanation of this is here impossible; but it can be understood how we thus prove absolutely that the rings are due to the mutual actions of the rays of light reflected from both surfaces of the film. We may prove this in yet another way, by substituting for the glass and metal surface, two glasses of widely different refractive powers, whose polarising angles are therefore also different (§ 120). We can then adjust the beam of light to either, and in either case, or by destroying reflection from either surface of the film, we destroy the rings. This last method of demonstration is, however, only suitable for private experiment.

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101. Spectrum Analysis of the Rings.-We further beautifully illustrate the matter by bringing to bear our neverfailing method of spectrum analysis. Cover the pair of Newton's lenses with a disc of black paper or card, having in it a slit, say, of an inch wide, and reaching all across, exactly over the centre; the slit then crosses all the bands at right angles, and the appearance, or image on the screen when focused there, is like one of the bands in Fig. 101. The whole arrangements are shown in plan in Fig. 102. The lantern must be turned considerably away from the screen, so that the reflected beam may have a small angle of incidence; or else, as the glasses are so thick, the light from the film will not be able to emerge from the narrow slit by which

it enters, and there will be only an image of a white slit as reflected from the upper surface of the top glass, and none of the portions of rings, which is what we want. The black disc is placed on the face of the lenses, L, with the slit perpendicular,

and the reflected slit is focused by the loose lens, F, at about the screen distance, but must be considerably divergent from the screen to allow for refraction by the prism, P, which gives the spectrum on the screen, s. The lenses are drawn much larger in proportion for the sake of clearness.

Now we know that if we use red light we get transverse bands of red and black; and that blue light gives us narrower bands, and closer together, of blue and black, as shown at R and B, Fig. 101. If, then, we pass the image of the

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