On alternative methods of determining Radius of Curvature using Newton s Rings set up

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1 Inernaional Leers of Chemisry, Physics and Asronomy Online: ISSN: , Vol. 48, pp 7-31 doi: / 0 SciPress Ld., Swizerland On alernaive mehods of deermining Radius of Curvaure using Newon s Rings se up K. H. Raveesha 1 *, Kamal Kumar, B. K. Prasad 3 1 Dep. of Physics, CMR Insiue of Technology, Bangalore Dep. of Mahemaics, CMR Insiue of Technology, Bangalore 3 Dep of Physics, CMR Insiue of Technology, Bangalore * address: 1 hod.physics@cmri.ac.in, Kamal.k@cmri.ac.in, 3 Prasad.bk@cmri.ac.in ABSTRACT I well known ha radius of curvaure of a plano convex lens can be deermined using Newon s Rings se up making use of Inerference by division of ampliude principle. The general mehod widely used involves measuremen of diameer of several circular dark fringes. We propose wo alernaive mehods involving differen formulae. I is based on he fac ha, he formaion of brigh and dark inerference fringes is a measure of he hickness of he air film a ha poin. The mehods use simpler geomery and he formulae are easier o derive. We presen he experimenal daa. The resuls from he experimen are in agreemen wih resuls obained hrough he general mehod. Keywords: Plano convex lens; Inerference; fringes; desrucive inerference; consrucive inerference 1. INTRODUCTION I is well known Newon described he formaion of brigh and dark rings using he plano convex lens [1]. I is undersood ha when a monochromaic beam of ligh falls normally on a Plano-convex lens kep on an opically plane glass plae, concenric brigh and dark circular fringes are formed due o he consrucive and desrucive inerference of ligh waves refleced from he lower surface of he lens and he upper surface of he plane glass plae. Formaion of a brigh or dark fringe a a poin depends on he hickness of he air film a ha poin (which creaes pah difference)[]. Convenionally Newon s rings experimen is used o deermine he radius of curvaure of a plano convex lens. The general mehod widely used involves measuremen of he diameer of several fringes. I is described in he secion. We have described wo alernaive mehods o deermine radius of curvaure in secion 3 & 4 wih deailed experimenal daa and analysis. The resuls obained by he alernaive mehods are in close agreemen wih ha obained hrough he general mehod. Conclusions are presened in secion 5. SciPress applies he CC-BY 4.0 license o works we publish: hps://creaivecommons.org/licenses/by/4.0/

2 8 Volume 48. GENERAL METHOD TO FIND RADIUS OF CURVATURE OF PLANO CONVEX LENS Seing up he Newons rings, he diameer of nd, 4 h, 6 h, 8 h, 10 h and1 h dark fringes are calculaed. If d m and d n represen he diameer of he m h and n h dark fringe, he radius of curvaure is deermined using he formula d m d n R 4.( m n) For he given planoconvex lens, he value of R is found hrough his mehod is 0.93m (manufacurer has prescribed he value as 1m). 3. ALTERNATIVE METHOD 1 TO FIND RADIUS OF CURVATURE This mehod involves he measuremen of radius of a clearly visible dark fringe preferable away from he cenre. By knowing he fringe number, he hickness of he air film which creaes he pah difference causing he desrucive inerference leading o he formaion of ha dark fringe is calculaed. Radius of curvaure is obained from he formula which is easily derived from rignamerical relaionships. I is assumed ha he radius of curvaure is large in comparison wih he pah difference. Figure 1. Newon s rings se up.

3 Inernaional Leers of Chemisry, Physics and Asronomy Vol Theory From he figure (1), r (ab ) (1) ab r () an 1 ( r ) (3) From rignamery, ssuming ab o be very small, R. ab R ab (4) where R is he radius of curvaure of he plano convex lens Figure. Circle geomery.

4 30 Volume 48 Experimenal daa, analysis and resuls From he condiion for he formaion of dark fringe (desrucive inerference) (n 1) n where is he hickness of he air film causing he formaion of dark fringe λ is he wavelengh of ligh used in he experimen (5896 x m) For h dark fringe, n = x m (5) Disance from he cenre o he h dark fringe in he experimen is r =.90 x10-3 m (6) From (), 3 ab (.9 10 ) ( ) m From (3), an ( ) radian From (4), Radius of curvaure R 0. 96m Where as we have considered he h dark fringe for our calculaions, any clearly visible fringe could be considered. 4. ALTERNATIVE METHOD TO FIND RADIUS OF CURVATURE This involves idenifying a clearly visible dark fringe (say h dark fringe as in he previous case) and calculaing he hickness of air film creaing he pah difference causing he formaion of dark fringe. The formula used is derived from using geomerical relaionships. From figure (1) Simplificaion yields ( R r R )

5 Inernaional Leers of Chemisry, Physics and Asronomy Vol Radius of curvaure For h dark fringe, n =, From (5) & (6) R r 4.4x 10 m (7) Disance from he cenre o he h dark fringe in he experimen is r =.90 x10-3 m Subsiuing hese parameers in (7) R R 0.95m (.9010 I may be noed ha he radius of curvaure obained from he alernaive mehods (1) & () are in close agreemen (0.96m & 0.95m respecively) wih he resul obained hrough he general mehod (0.93m). 3 ) 5. CONCLUSIONS Two alernaive mehods o deermine he radius of curvaure are presened. The resuls obained are in close agreemen. The wo proposed mehods are relaively easier as hey involve measuremen relaed o one fringe as compared o measuremens relaed o 6 fringes in he general mehod. Based on he auhors ineracions wih several suden groups a undergraduae level, i may be menioned ha sudens while conducing hese experimenal mehods are able o develop an appreciaion on how rigonomery can be uilized o develop simpler alernaive mehods. These alernaive mehods may be paricularly useful in Indusrial siuaions where radius of curvaure many plano convex lenses are o deermined in a shor duraion of ime as hese mehods involve lesser measuremens (one fringe) and hence auomaion is easier. Acknowledgemens The auhors are deeply indebed o he auhoriies of CMR Insiue of Technology, Bangalore for offering necessary laboraory and library faciliies which resuled in his research work. References [1] Ajoy Ghaak, 1991, Opics,Taa Mcgraw Hill publicaion, 3 rd Ediion, [] Chaopadhyay, 00, An advanced course in Pracical Physics, Cenral Publicaion, 6 h Ediion, 7 ( Received 17 February 0; acceped 4 February 0 )

6 Volume / On Alernaive Mehods of Deermining Radius of Curvaure Using Newon s Rings Se up /