Measurement of the Waves of Light
The diffraction fringes described in Lecture II., instead of being formed on the retina, may be formed on a screen, or upon ground glass, when they can be looked at through a magnifying lens from behind, or they can be observed in the air when the ground glass is removed. Instead of permitting them to form on the retina, we will suppose them formed on a screen. This places us in a condition to understand, even without trigonometry, the solution of the important problem of measuring the length of a wave of light.
We will suppose the screen so distant that the rays falling upon it from the two margins of the slit are sensibly parallel. We have learned in Lecture II. that the first of the dark bands corresponds to a difference of marginal path of one undulation; the second dark band to a difference of path of two undulations; the third dark band to a difference of three undulations, and so on. Now the angular distance of the bands from the centre is capable of exact measurement; this distance depending, as already stated, on the width of the slit. With a slit 1.35 millimeter wide,29 Schwerd found the angular distance of the first dark band from the centre of the field to be 1’38”; the angular distances of the second, third, fourth dark bands being twice, three times, four times this quantity.
Let A B, fig. 57, be the plate in which the slit is cut, and C D the grossly exaggerated width of the slit, with the beam of red light proceeding from it at the obliquity corresponding to the first dark band. Let fall a perpendicular from one edge, D, of the slit on the marginal ray of the other edge at d. The distance, C d, between the foot of this perpendicular and the other edge is the length of a wave of the light. The angle C D d, moreover, being equal to R C R’, is, in the case now under consideration, 1’38”. From the centre D, with the width D C as radius, describe a semicircle; its radius D C being 1.35 millimeter, the length of this semicircle is found by an easy calculation to be 4.248 millimeters. The length C d is so small that it sensibly coincides with the arc of the circle. Hence the length of the semicircle is to the length C d of the wave as 180° to 1’38”, or, reducing all to seconds, as 648,000” to 98”. Thus, we have the proportion—
648,000: 98:: 4.248 to the wave-length C d.
Making the calculation, we find the wave-length for this particular kind of light to be 0.000643 of a millimeter, or 0.000026 of an inch.
Footnotes
1 Among whom may be especially mentioned the late Sir Edmund Head, Bart., with whom I had many conversations on this subject.
2 At whose hands it gives me pleasure to state I have always experienced honourable and liberal treatment.
3 One of the earliest of these came from Mr. John Amory Lowell of Boston.
4 It will be subsequently shown how this simple apparatus may be employed to determine the ‘polarizing angle’ of a liquid.
5 From this principle Sir John Herschel deduces in a simple and elegant manner the fundamental law of reflection.—See Familiar Lectures, p. 236.
6 The low dispersive power of water masks, as Helmholtz has remarked, the imperfect achromatism of the eye. With the naked eye I can see a distant blue disk sharply defined, but not a red one. I can also see the lines which mark the upper and lower boundaries of a horizontally refracted spectrum sharp at the blue end, but ill-defined at the red end. Projecting a luminous disk upon a screen, and covering one semicircle of the aperture with a red and the other with a blue or green glass, the difference between the apparent sizes of the two semicircles is in my case, and in numerous other cases, extraordinary. Many persons, however, see the apparent sizes of the two semicircles reversed. If with a spectacle glass I correct the dispersion of the red light over the retina, then the blue ceases to give a sharply defined image. Thus examined, the departure of the eye from achromatism appears very gross indeed.
7 Both in foliage and in flowers there are striking differences of absorption. The copper beech and the green beech, for example, take in different rays. But the very growth of the tree is due to some of the rays thus taken in. Are the chemical rays, then, the same in the copper and the green beech? In two such flowers as the primrose and the violet, where the absorptions, to judge by the colours, are almost complementary, are the chemically active rays the same? The general relation of colour to chemical action is worthy of the application of the method by which Dr. Draper proved so conclusively the chemical potency of the yellow rays of the sun.
8 Young, Helmholtz, and Maxwell reduce all differences of hue to combinations in different proportions of three primary colours. It is demonstrable by experiment that from the red, green, and violet all the other colours of the spectrum may be obtained.
Some years ago Sir Charles Wheatstone drew my attention to a work by Christian Ernst Wünsch, Leipzig 1792, in which the author announces the proposition that there are neither five nor seven, but only three simple colours in white light. Wünsch produced five spectra, with five prisms and five small apertures, and he mixed the colours first in pairs, and afterwards in other ways and proportions. His result is that red is a simple colour incapable of being decomposed; that orange is compounded of intense red and weak green; that yellow is a mixture of intense red and intense green; that green is a simple colour; that blue is compounded of saturated green and saturated violet; that indigo is a mixture of saturated violet and weak green; while violet is a pure simple colour. He also finds that yellow and indigo blue produce white by their mixture. Yellow mixed with bright blue (Hochblau) also produces white, which seems, however, to have a tinge of green, while the pigments of these two colours when mixed always give a more or less beautiful green, Wünsch very emphatically distinguishes the mixture of pigments from that of lights. Speaking of the generation of yellow, he says, ‘I say expressly red and green light, because I am speaking about light-colours (Lichtfarben), and not about pigments.’ However faulty his theories may be, Wünsch’s experiments appear in the main to be precise and conclusive. Nearly ten years subsequently, Young adopted red, green, and violet as the three primary colours, each of them capable of producing three sensations, one of which, however, predominates over the two others. Helmholtz adopts, elucidates, and enriches this notion. (Popular Lectures, p. 249. The paper of Helmholtz on the mixture of colours, translated by myself, is published in the Philosophical Magazine for 1852. Maxwell’s memoir on the Theory of Compound Colours is published in the Philosophical Transactions, vol. 150, p. 67.)
9 The following charming extract, bearing upon this point, was discovered and written out for me by my deeply lamented friend Dr. Bence Jones, when Hon. Secretary to the Royal Institution:—
‘In every kind of magnitude there is a degree or sort to which our sense is proportioned, the perception and knowledge of which is of the greatest use to mankind. The same is the groundwork of philosophy; for, though all sorts and degrees are equally the object of philosophical speculation, yet it is from those which are proportioned to sense that a philosopher must set out in his inquiries, ascending or descending afterwards as his pursuits may require. He does well indeed to take his views from many points of sight, and supply the defects of sense by a well-regulated imagination; nor is he to be confined by any limit in space or time; but, as his knowledge of Nature is founded on the observation of sensible things, he must begin with these, and must often return to them to examine his progress by them. Here is his secure hold: and as he sets out from thence, so if he likewise trace not often his steps backwards with caution, he will be in hazard of losing his way in the labyrinths of Nature.’—(Maclaurin: An Account of Sir I. Newton’s Philosophical Discoveries. Written 1728; second edition, 1750; pp. 18, 19.)
10 I do not wish to encumber the conception here with the details of the motion, but I may draw attention to the beautiful model of Prof. Lyman, wherein waves are shown to be produced by the circular motion of the particles. This, as proved by the brothers Weber, is the real motion in the case of water-waves.
11 Copied from Weber’s Wellenlehre.
12 See Lectures on Sound, 1st and 2nd ed., Lecture VII.; and 3rd ed., Chap. VIII. Longmans.
13 Boyle’s Works, Birch’s edition, p. 675.
14 Page 743.
15 The beautiful plumes produced by water-crystallization have been successfully photographed by Professor Lockett.
16 In a little volume entitled ‘Forms of Water,’ I have mentioned that cold iron floats upon molten iron. In company with my friend Sir William Armstrong, I had repeated opportunities of witnessing this fact in his works at Elswick, 1863. Faraday, I remember, spoke to me subsequently of the perfection of iron castings as probably due to the swelling of the metal on solidification. Beyond this, I have given the subject no special attention; and I know that many intelligent iron-founders doubt the fact of expansion. It is quite possible that the solid floats because it is not wetted by the molten iron, its volume being virtually augmented by capillary repulsion. Certain flies walk freely upon water in virtue of an action of this kind. With bismuth, however, it is easy to burst iron bottles by the force of solidification.
17 This beautiful law is usually thus expressed: The index of refraction of any substance is the tangent of its polarizing angle. With the aid of this law and an apparatus similar to that figured at page 15, we can readily determine the index of refraction of any liquid. The refracted and reflected beams being visible, they can readily be caused to inclose a right angle. The polarizing angle of the liquid may be thus found with the sharpest precision. It is then only necessary to seek out its natural tangent to obtain the index of refraction.
18 Whewell.
19 Removed from us since these words were written.
20 The only essay known to me on the Undulatory Theory, from the pen of an American writer, is an excellent one by President Barnard, published in the Smithsonian Report for 1862.
21 Boyle’s Works, Birch’s edition, vol. i. pp, 729 and 730.
22 Werke, B. xxix. p. 24.
23 Defined in Lecture I.
24 This circumstance ought not to be lost sight of in the examination of compound spectra. Other similar instances might be cited.
25 The dark band produced when the sodium is placed within the lamp was observed on the same occasion. Then was also observed for the first time the magnificent blue band of lithium which the Bunsen’s flame fails to bring out.
26 New York: for more than a decade no such weather had been experienced. The snow was so deep that the ordinary means of locomotion were for a time suspended.
27 ‘Il faut reconnaître que parmi les peuples civilisés de nos jours il en est pen chez qui les hautes sciences aient fait moins de progrès qu’aux États-Unis, ou qui aient fourni moins de grands artistes, de poëtes illustres et de célèbres écrivains.’ (De la Démocratie en Amérique, etc. tome ii. p. 36.)
28 At these points the two rectangular vibrations into which the original polarized ray is resolved by the plates of gypsum, act upon each other like the two rectangular impulses imparted to our pendulum in Lecture IV., one being given when the pendulum is at the limit of its swing. Vibration is thus converted into rotation.
29 The millimeter is about 1/25th of an inch.