A Note on Newton's Measurements of Film Thicknesses and Their Corresponding(Interference) ColoursAuthor(s): Christopher HammondSource: Notes and Records of the Royal Society of London, Vol. 55, No. 3 (Sep., 2001), pp. 391-394Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/531948 .

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Notes Rec. R. Soc. Lond. 55 (3), 391-394 (2001)

A NOTE ON NEWTON'S MEASUREMENTS OF FILM THICKNESSES

AND THEIR CORRESPONDING (INTERFERENCE) COLOURS

by

CHRISTOPHER HAMMOND

Department of Materials, University of Leeds, Leeds, LS2 9JT, UK

Newton's Opticks is a classic of scientific literature which is readily accessible to the general reader and from which his powers of observation, measurement and deduction may be recognized unequivocally. The fourth (1730) edition, last reprinted by Dover Publications in 1979, includes a Preface by I. Bernard Cohen, a Foreword by Albert Einstein and an Introduction by Sir Edmund Whittaker. More recently A. Rupert Hall's All Was Light: An Introduction to Newton s Opticks1 provides a comprehensive review and analysis of the book, its preparation and subsequent reception.

The object of this note is to examine a small but significant part of Newton's work in the Opticks, that of his measurements of the thicknesses of air, water and muscovy glass (i.e. muscovite) films and their corresponding interference colours, which appear in Parts I and II of the second book.

In Part I of the second book, Newton describes his 'Observations concerning the Reflexions, Refractions and Colours of thin transparent Bodies'. In particular, 'Obs 4' includes his well-known description of the (interference) colours arising from the contact between two telescope object-glasses: one a plano-convex for a 14-foot (focal length) telescope, the other a large double-convex object glass for a telescope of about 50-feet focal length. The ring pattern seen by reflected light when the plane and curved surfaces of the object-glasses 'were most compress'd so as to make the black Spot appear in the center' is represented on p. 199 of the fourth edition. 'Obs 5' and 'Obs 6' include Newton's estimates of the thicknesses of the air films by which each colour is produced and his demonstration that the 'most luminous Parts of all the brightest Rings' occur in the arithmetical progression of 1/178000, 3/178000, 5/178000, 7/178000, 1/178000, etc. parts of an inch.

In 'Obs 10', Newton notes the contraction in the diameters of the rings when water is intruded into the air gap between the glass surfaces, and shows that the ratio of the diameters, which he estimates as 3 to 4, are 'as the Sines which measure the Refraction made out of that Medium into Air'. 'Obs 16' to 'Obs 19' again include his well-known, beautiful and exact descriptions of the cblours exhibited by soap bubbles and thin plates of muscovy glass (muscovite), i.e. 'the Appearances of a denser Medium thin'd within a rarer'. He also notes that the same sequence of colours are observed on heating 'polished Steel ... or on Bell-metal or some other metalline Substances', and surmises that these are caused by the formation 'of a thin glassy skin'

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© 2001 The Royal Society

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Christopher Hammond

(i.e. the growth of a thin metal oxide). The wide range of Newton's observations reminds us of his great practical ability.

Part II of the second book, 'Remarks upon the foregoing Observations', consists of a summary and analysis of the observations made in Part I. Newton confirms that the most luminous parts of the rays (in reflected light) are of a bright yellow citrine colour or 'confine of orange and yellow'. He recognizes that his estimates of the ratios of the thicknesses of water and (muscovy) glass to air, which produce the same colours (3/4 for water and 20/31 for glass), determined from measurements of 'Refraction of the mean refrangible Ray', may vary for 'other sorts of Rays', but that the differences are small. In short, he recognizes that his estimates of the refractive indices of water (4/3 = 1.33) and muscovy glass (31/20= 1.53) are slightly wavelength- dependent.

On these Grounds I have composed the following Table, wherein the thickness of Air, Water and Glass, at which each Colour is most intense and specifick, is expressed in parts of an Inch divided into ten hundred thousand equal parts.

This table, for reflected light, is reproduced from p. 233 of the fourth edition. The sequence of colours, but not their spacing, is identical to that in the Michel-Levy chart, which is widely used in polarized light microscopy.2 The interference colours in the chart correspond to those shown by a quartz wedge set at 45° between crossed polars with black (zero thickness), as in Newton's table, at the top. Newton divided the sequence of interference colours into orders, each order being terminated by a distinctive red-violet 'sensitive tint' colour (which arise from the destructive interference of the yellow-green components of white light). In Newton's experiments, the orders become more closely spaced because of the curvature of the lens surfaces, whereas the Michel-Levy chart has the advantage that they are evenly spaced. The vertical and radiating lines in the chart are used in polarized light microscopy as an aid to the identification of minerals in thin sections.

The numerical values of the red sensitive tints in Newton's table may be compared with those in the Michel-Levy chart, which are expressed in terms of optical path differences (OPD). For an air film of thickness t between two (glass) surfaces, the OPD=2t+ 1/2X; 2t because in reflected light the wave travels both ways through the air film, and 1/2X to take account of the path difference (or 180° phase change) which occurs between the waves reflected at the glass/air and air/glass surfaces. For destructive interference, the OPD= 1/2k, 3/2k, 5/2k ..., which correspond to 2t values of OX, 1X, 2 ....

The air film thickness values which terminate each order, interpolated from Newton's data, are shown in the first column of the supplementary table; the corresponding 2t values, expressed in nanometres, in the second column and the corresponding OPD values from the Michel-Levy chart are given in the third column. As can be seen, Newton's data are remarkably accurate. Similarly, if we compare Newton's air film thicknesses which show the bright yellow citrine colour (1/178000, 3/178000, 5/178000 ... parts of an inch) to the corresponding values in the Michel-Levy chart, we find 2t values of 285nm (332nm), 856 nm (866nm) and 1427

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Newton 's measurements offilm thicknesses

Figure 1. Newton's table (left) of the orders of the (interference) colours with the corresponding thicknesses expressed as 10-6 inch, and a supplementary table (right) showing the comparison between Newton's 2t values, the corresponding OPD values from the Michel-Levy chart and,

for each colour, the corresponding values of the refractive indices of water and muscovite.

nm (1430nm)-the Michel-Levy values being given in brackets. Again, the agreement is very close.

The refractive indices of water and muscovite, determined from Newton's air-water and air-glass thickness measurements, are given in the two right-hand columns of the supplementary table. For water these are fairly consistently 1.333, the present accepted value; for muscovite there is a little more scatter around 1.555. Muscovite is an optically biaxial material; however, for unpolarized light travelling perpendicular to the cleavage faces the birefringence-the difference between the f3 and y refractive indices-is small. P values for yellow-green light lie in the range 1.580-1.610 and y values in the range 1.587-1.616.3 The lower values, which correspond most closely with Newton's measurements, are characteristic of the so-called rose muscovites with low iron (particularly Fe3+) and low manganese contents, which suggests that it was such a type of muscovite that Newton actually used, although in the very thin cleavage sections the pink/rose colour would not have been readily apparent.

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394 Christopher Hammond

NOTES

1 A. Rupert Hall, All Was Light: An Introduction to Newton s Opticks (Clarendon Press, Oxford, 1993).

2 See for example, N.H. Hartshome and A. Stuart, Crystals and the Polarising Microscope, 4th edn (Edward Arnold, London, 1970).

3 Data from: W.A. Deer, R.A. Howie and J. Zussman, An Introduction to the Rock-Forming Minerals, 2nd edn (Longman, 1992).

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