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Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces—a spherical surface and an adjacent touching flat surface. It is named for Isaac Newton, who first studied the effect in 1717. When viewed with monochromatic light, Newton's rings appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. When viewed with white light, it forms a concentric ring pattern of rainbow colors, because the different wavelengths of light interfere at different thicknesses of the air layer between the surfaces.
The bright rings are caused by constructive interference between the light rays reflected from both surfaces, while the dark rings are caused by destructive interference. Moving outwards from one bright ring to the next, the path difference of interfering rays at the given radius is one wavelength, λ, corresponding to an increase of thickness of the air layer between the glass surfaces by λ/2. For glass surfaces that are not spherical, the fringes will not be rings but will have other shapes.
For illumination from above, with a dark center, the radius of the Nth bright ring is given by
where N is the bright-ring number, R is the radius of curvature of the glass lens the light is passing through, and λ is the wavelength of the light.
The above formula is also applicable for dark rings for the ring pattern obtained by transmitted light.
Consider light incident on the flat plane of the convex lens that is situated on the optically flat glass surface below. The light passes through the glass lens until it comes to the glass-air boundary, where the transmitted light goes from a higher refractive index (n) value to a lower n value. The transmitted light passes through this boundary with no phase change. The reflected light (about 4% of the total) also has no phase change. The light that is transmitted into the air travels a distance, t, before it is reflected at the flat surface below; reflection at the air-glass boundary causes a half-cycle phase shift because the air has a lower refractive index than the glass. The reflected light at the lower surface returns a distance of (again) t and passes back into the lens. The two reflected rays will interfere according to the total phase change caused by the extra path length 2t and by the half-cycle phase change induced in reflection at the lower surface. When the distance 2t is less than a wavelength, the waves interfere destructively, hence the central region of the pattern is dark.
A similar analysis for illumination of the device from below instead of from above shows that in that case the central portion of the pattern is bright, not dark. (Compare the given example pictures to see this difference.)
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.
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.
- 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. doi:10.1080/14786443308647959. 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. doi:10.1046/j.1475-1313.1998.00366.x. ISSN 0275-5408.
- Dobroiu, Adrian; Alexandrescu, Adrian; Apostol, Dan; Nascov, Victor; Damian, Victor S. (2000). "Improved method for processing Newton's rings fringe patterns". 4068: 342–347. doi:10.1117/12.378693. ISSN 0277-786X.
- 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. doi:10.1080/14786444408521466. ISSN 1941-5982.
|Wikimedia Commons has media related to Newton's rings.|
- Newton’s Ring from Eric Weisstein's World of Physics
- Explanation of and expression for Newton's rings
- Newton's rings Video of a simple experiment with two lenses, and Newton's rings on mica observed. (On the website FizKapu.) (Hungarian)