International projectionist (Jan 1943-Dec 1944)

Newton's Rings --The Yardsticks Of Optical Science t IN the irridescence of an oil film on a wet city pavement and in the colors of a soap bubble in the sunlight, science and industry have the key to the most precise and delicate direct measuring method known. "It has been observed by others, that transparent Substances, such as Glass, Water, Air, etc., when made very thin by being blown into Plates, do exhibit various Colours, according to their various thinness, although at a greater thickness they appear very clear and colourless." So wrote Sir Isaac Newton in the last quarter of the Seventeenth Century and then he sets about describing a series of experiments in what we now call physical optics which have not been surpassed in ingenuity to date. Considering the crudity of his apparatus, the accuracy of his results is amazing. The dimensioning of mechanical parts for high grade optical apparatus is very precise. For instance, the lens separations in a modern microscope objective are specified in thousandths of a millimeter, or microns, one of which equals 0.00004". But for gauging optical surfaces on lenses, prisms, and reflectors, the micron, small as it is, is still too large. Here recourse must be taken to fractions of the wavelength of light. The optical engineer assumes and the skilled optical craftsman attains in routine production accuracies of curve to 0.000 006" and can exceed in fineness 0.000 000 8" when instrumental applications require it. How can optical work be measured confidently with such delicacy? "It's very simple," says the experienced lens grinder and polisher. "I measured it by Newton's Rings and it's within a quarter or a tenth or a thirtieth of a wavelength." In the color phenomena of thin wedge films he has a means for measuring the accuracy of transmitting and reflecting surfaces in units which, though real, are so small as to be almost inconceivable. Each time such a measurement is made, the classical experiments of Newton are duplicated. This makes it interesting to follow through with the Newtonian explanation as a prelude to the modern explanation. Newton was not the first to observe the formation of colored areas in the thin film of air between two polished plates, f'Bausch & Lomb Magazine. By RUDOLPH MILLER or in thin layers of water as in soap bubbles, or thin plates of glass, mica or pitch. Nor was he the first to propose an explanation. Robert Boyle and Hooke, the microscopist, both preceded him. Neither one, however, provided .an explanation on a definite quantitative basis. f r s „ FIGURE 1 "To observe more nicely the colours" under controlled conditions, Newton placed the plane surface of a planoconvex objective from a fourteen-foot telescope on the convex surface of a bi-convex objective from a telescope of about fifty-foot focus, thereby forming a thin film of air which gradually increased in thickness from zero. On observing this arrangement by reflected light, at the center where the surfaces were in contact he saw a black circular spot about which was a series of bright and dark concentric circles. In white light the bright rings were colored. In red light the rings were larger than when viewed in blue light. By calculating the distance between the glass surfaces he was able to determine the air film thickness responsible for each color. Figure 1, taken from "Newton's Opticks," shows the sequence of colors in 8 ~o the bright rings surrounding the central dark spot; a, b, c, d, e: f, g, h, i, k: 1, m, n, o, p: q, r, s, t: v, x: y, z, denote the colors in order from the center, black, blue, white, yellow, red: violet, blue, green, yellow, red: purple, blue, green, yellow, red: green, red: greenish blue, reddish white. Figure 2, from the same source shows the color sequence when the rings are viewed by reflected and transmitted light. Newton's Calculations Figure 3 shows the geometry involved in determining the thickness of the air film at any point. Let r = radius of the colored or black ring R = radius of curvature of the convex surface t = thickness of film at distance r from center thenr2 = R2 — (R — t)2 r2 = R2_(R2_2Rt + t2) r2 — R2 — R2 + 2Rt — t2 r2 = 2Rt — t2 t2, being small, is ignored r2 therefore t = 2R In this way Newton calculated the thickness of the air film responsible for the production of each colored ring. He determined the thickness for each dark and bright ring surrounding the central dark area when essentially monochromatic light was used and found that the thickness for each successive ring was greater by a fixed amount. Thus if the thickness for the first dark ring was t, that of the second was 2t, the third 3t, and so on. From the same data it was evident that the thicknesses corresponding to the bright rings were y2t, iy2t, 2%t. Combining these quantitative findings fctfSs S K; _ C: fe FIGURE 2. Colors by reflected light above . . . by transmitted light below. JANUARY 1943