133.35.116.82: /* Properties */

2014-12-05T14:01:15Z

Properties

en>Quondum: {{nowrap}}

2013-10-04T17:00:02Z

← Older revision		Revision as of 19:00, 4 October 2013
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	~~Let me initial start~~ by ~~introducing myself~~. ~~My title~~ is ~~Boyd Butts even though~~ it ~~is not~~ the ~~name on my~~ [~~http~~:/~~/Std~~.~~About~~.~~com~~/od/~~overviewofstds~~/~~a/testessential~~.~~htm birth certificate]~~. ~~For many years he~~'s ~~been residing~~ in ~~North Dakota~~ and his ~~family enjoys~~ it. ~~Bookkeeping~~ is ~~her working~~ [~~http~~:~~//www~~.~~Care2~~.~~com/greenliving/5~~-~~myths~~-~~about~~-~~herpes~~.~~html day occupation] now~~. ~~What I love std testing~~ at ~~home doing~~ is to ~~collect badges std home test but std testing~~ at ~~home I~~'~~ve been using on new things lately.~~<br><br>~~my website~~; ~~std home test -~~ [~~https~~://www.~~silvercreekpreschool~~.ca/~~rid-your-pc-itd-internet-transmitted-diseases look at more info~~],		[[File:20cm Air 1.jpg\|thumb\|Newton's rings observed through a microscope. The smallest increments on the superimposed scale are 100μm.]]
			[[File:Newton's_rings_(650nm_red_laser_light).jpeg\|thumb\|"Newton’s rings" interference pattern created by a plano-convex lens illuminated by 650nm red laser light, photographed using a low-power microscope.]]

			'''Newton's rings''' is a phenomenon in which an [[Interference (wave propagation)\|interference]] pattern is created by the [[reflection (physics)\|reflection]] of [[light]] between two surfaces—a [[sphere\|spherical]] surface and an adjacent flat surface. It is named after [[Isaac Newton]], who first studied them in 1717. When viewed with [[monochrome\|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 [[wavelength]]s of light interfere at different thicknesses of the air layer between the surfaces.

			[[Image:Optical flat interference.svg\|thumb\|left\|upright=1.4\|How the interference fringes form. ]]

			The light rings are caused by constructive interference between the light rays reflected from both surfaces, while the dark rings are caused by destructive interference. Also, the outer rings are spaced more closely than the inner ones. Moving outwards from one dark ring to the next, for example, increases the path difference by the same amount, ''λ'', corresponding to the same increase of thickness of the air layer, ''λ''/2. Since the slope of the convex lens surface increases outwards, separation of the rings gets smaller for the outer rings. For surfaces that are not convex, the fringes will not be rings but will have other shapes.

			The radius of the ''N''<sup>th</sup> Newton's bright ring is given by
			:<math> r_N= \left[\left(N - {1 \over 2}\right)\lambda R\right]^{1/2}, </math>
			where
			''N'' is the bright-ring number, ''R'' is the [[radius of curvature (mathematics)\|radius of curvature]] of the lens the light is passing through, and ''λ'' is the wavelength of the light passing through the glass.

			[Note that the figure at left has the sign of the interference backward. There's a sign change in the fields reflected at the second interface but not at the first interface, reversing the interference pattern from that shown. The limiting case, at the center of the pattern, is equivalent to no gap, and hence like a continuous, non-reflecting medium, consistent with the famous dark reflection spot, as seen in the picture on the right.]

			The phenomenon was first described by [[Robert Hooke]] in his 1664 book ''[[Micrographia]]'', although its name derives from the physicist Isaac Newton, who was the first to analyze it.

			The above formula is applicable only for Newton's rings obtained by reflected light.

			==Theory==
			[[File:Newton's rings 02.svg\|thumb\|The experimental setup: a convex lens is placed on top of a flat surface.]]
			[[File:Newton rings.jpg\|thumb\|Newton's rings seen in two plano-convex lenses with their flat surfaces in contact. One surface is slightly convex, creating the rings. In white light, the rings are rainbow-colored, because the different wavelengths of each color interfere at different locations.]]

			There is 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, and here the light goes from a higher refractive index (''n'') value to a lower ''n'' value. The light passes through this boundary and suffers no phase change. Also at this boundary, some light is transmitted into the air, and some light is reflected. The light that is transmitted to the air travels a distance, ''t'', before it is reflected at the flat surface below; the air-glass boundary causes a half-cycle phase shift because the air has a lower refractive index than the glass. The two reflected rays now travel in the same direction to be detected. The convex lens touches the flat surface below, and from this point, as one gets farther away, the distance ''t'' increases, because the lens is curving away from the surface:

			:<math>2Rt = t^2 + x</math>

			:<math>t\ll x</math> so <math>t^2\lll x</math> therefore:

			:<math>2t = {X \over R}</math> and finally, we have:

			:<math>t = {X \over 2R}</math>

			==External links==
			*{{Commons category-inline\|Newton's rings}}
			*[http://scienceworld.wolfram.com/physics/NewtonsRings.html Newton’s Ring from Eric Weisstein's World of Physics]
			*[http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/NewtonsRings/NewtonsRings.html Photos]
			*[http://www.citycollegiate.com/newtons_rings.htm Explanation of and expression for Newton's rings]
			*[http://www.fizkapu.hu/fizfilm/fizfilm6.html Newton's rings] Video of a simple experiment with two lenses, and Newton's rings on mica observed. (On the website [http://www.fizkapu.hu FizKapu].) {{hu}}

			[[Category:Optics]]

en>Quondum: /* General bilinear forms */ Refining the statements as per the reference.

2012-08-12T17:20:01Z

General bilinear forms: Refining the statements as per the reference.

New page

Let me initial start by introducing myself. My title is Boyd Butts even though it is not the name on my [http://Std.About.com/od/overviewofstds/a/testessential.htm birth certificate]. For many years he's been residing in North Dakota and his family enjoys it. Bookkeeping is her working [http://www.Care2.com/greenliving/5-myths-about-herpes.html day occupation] now. What I love std testing at home doing is to collect badges std home test but std testing at home I've been using on new things lately.<br><br>my website; std home test - [https://www.silvercreekpreschool.ca/rid-your-pc-itd-internet-transmitted-diseases look at more info],

Orthogonal complement - Revision history

133.35.116.82: /* Properties */

en>Quondum: {{nowrap}}

en>Quondum: /* General bilinear forms */ Refining the statements as per the reference.