Newton's rings
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/fc/20cm_Air_1.jpg/220px-20cm_Air_1.jpg)
Newton's rings is a phenomenon in which an
History
The phenomenon was first described by Robert Hooke in his 1665 book Micrographia. Its name derives from the mathematician and physicist Sir Isaac Newton, who studied the phenomenon in 1666 while sequestered at home in Lincolnshire in the time of the Great Plague that had shut down Trinity College, Cambridge. He recorded his observations in an essay entitled "Of Colours". The phenomenon became a source of dispute between Newton, who favored a corpuscular nature of light, and Hooke, who favored a wave-like nature of light.[1] Newton did not publish his analysis until after Hooke's death, as part of his treatise "Opticks" published in 1704.
Theory
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/42/Optical_flat_interference.svg/310px-Optical_flat_interference.svg.png)
The pattern is created by placing a very slightly
Consider
A similar analysis for illumination of the device from below instead of from above shows that in this case the central portion of the pattern is bright, not dark, as shown in Fig. 1. When the light is not monochromatic, the radial position of the fringe pattern has a "rainbow" appearance, as shown in Fig. 5.
Constructive interference
(Fig. 4a): In areas where the path length difference between the two rays is equal to an odd multiple of half a
Destructive interference
(Fig. 4b): At other locations, where the path length difference is equal to an even multiple of a half-wavelength, the reflected waves will be 180°
This interference results in a pattern of bright and dark lines or bands called "interference fringes" being observed on the surface. These are similar to contour lines on maps, revealing differences in the thickness of the air gap. The gap between the surfaces is constant along a fringe. The path length difference between two adjacent bright or dark fringes is one wavelength λ of the light, so the difference in the gap between the surfaces is one-half wavelength. Since the wavelength of light is so small, this technique can measure very small departures from flatness. For example, the wavelength of red light is about 700 nm, so using red light the difference in height between two fringes is half that, or 350 nm, about 1/100 the diameter of a human hair. Since the gap between the glasses increases radially from the center, the interference fringes form concentric rings. For glass surfaces that are not axially symmetric, the fringes will not be rings but will have other shapes.
Quantitative Relationships
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/de/AgfaDia.jpg/220px-AgfaDia.jpg)
For illumination from above, with a dark center, the radius of the Nth bright ring is given by
Given the radial distance of a bright ring, r, and a radius of curvature of the lens, R, the air gap between the glass surfaces, t, is given to a good approximation by
where the effect of viewing the pattern at an angle oblique to the incident rays is ignored.
Thin-film interference
The phenomenon of Newton's rings is explained on the same basis as thin-film interference, including effects such as "rainbows" seen in thin films of oil on water or in soap bubbles. The difference is that here the "thin film" is a thin layer of air.
References
- ISBN 0-521-23143-4.
- ISBN 978-0-321-69686-1.
Further reading
- Airy, G.B. (1833). "VI.On the phænomena of Newton's rings when formed between two transparent substances of different refractive powers". Philosophical Magazine. Series 3. 2 (7): 20–30. ISSN 1941-5966.
- Illueca, C.; Vazquez, C.; Hernandez, C.; Viqueira, V. (1998). "The use of Newton's rings for characterizing ophthalmic lenses". Ophthalmic and Physiological Optics. 18 (4): 360–371. S2CID 222086863.
- Dobroiu, Adrian; Alexandrescu, Adrian; Apostol, Dan; Nascov, Victor; Damian, Victor S. (2000). "Improved method for processing Newton's rings fringe patterns". In Necsoiu, Teodor; Robu, Maria; Dumitras, Dan C (eds.). SIOEL '99: Sixth Symposium on Optoelectronics. Vol. 4068. pp. 342–347. )
- Tolansky, S. (2009). "XIV. New contributions to interferometry. Part II—New interference phenomena with Newton's rings". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 35 (241): 120–136. ISSN 1941-5982.
External links
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
- Newton's Ring from Eric Weisstein's World of Physics
- Explanation of and expression for Newton's rings Archived 2014-11-19 at the Wayback Machine
- Newton's rings Video of a simple experiment with two lenses, and Newton's rings on mica observed. (On the website FizKapu.) (in Hungarian)