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

Transcription

1 International Letters of Cheistry, Physics and Astronoy Online: ISSN: , Vol. 48, pp 7-31 doi: / 0 SciPress Ltd., Switzerland On alternative ethods of deterining Radius of Curvature using Newton s Rings set up K. H. Raveesha 1 *, Kaal Kuar, B. K. Prasad 3 1 Dept. of Physics, CMR Institute of Technology, Bangalore Dept. of Matheatics, CMR Institute of Technology, Bangalore 3 Dept of Physics, CMR Institute of Technology, Bangalore *E-ail address: 1 hod.physics@crit.ac.in, Kaal.k@crit.ac.in, 3 Prasad.bk@crit.ac.in ABSTRACT It well known that radius of curvature of a plano convex lens can be deterined using Newton s Rings set up aking use of Interference by division of aplitude principle. The general ethod widely used involves easureent of diaeter of several circular dark fringes. We propose two alternative ethods involving different forulae. It is based on the fact that, the foration of bright and dark interference fringes is a easure of the thickness of the air fil at that point. The ethods use sipler geoetry and the forulae are easier to derive. We present the experiental data. The results fro the experient are in agreeent with results obtained through the general ethod. Keywords: Plano convex lens; Interference; fringes; destructive interference; constructive interference 1. INTRODUCTION It is well known Newton described the foration of bright and dark rings using the plano convex lens [1]. It is understood that when a onochroatic bea of light falls norally on a Plano-convex lens kept on an optically plane glass plate, concentric bright and dark circular fringes are fored due to the constructive and destructive interference of light waves reflected fro the lower surface of the lens and the upper surface of the plane glass plate. Foration of a bright or dark fringe at a point depends on the thickness of the air fil at that point (which creates path difference)[]. Conventionally Newton s rings experient is used to deterine the radius of curvature of a plano convex lens. The general ethod widely used involves easureent of the diaeter of several fringes. It is described in the section. We have described two alternative ethods to deterine radius of curvature in section 3 & 4 with detailed experiental data and analysis. The results obtained by the alternative ethods are in close agreeent with that obtained through the general ethod. Conclusions are presented in section 5. SciPress applies the CC-BY 4.0 license to works we publish:

2 8 Volue 48. GENERAL METHOD TO FIND RADIUS OF CURVATURE OF PLANO CONVEX LENS Setting up the Newtons rings, the diaeter of nd, 4 th, 6 th, 8 th, 10 th and1 th dark fringes are calculated. If d and d n represent the diaeter of the th and n th dark fringe, the radius of curvature is deterined using the forula d d n R 4.( n) For the given planoconvex lens, the value of R is found through this ethod is 0.93 (anufacturer has prescribed the value as 1). 3. ALTERNATIVE METHOD 1 TO FIND RADIUS OF CURVATURE This ethod involves the easureent of radius of a clearly visible dark fringe preferable away fro the centre. By knowing the fringe nuber, the thickness of the air fil which creates the path difference causing the destructive interference leading to the foration of that dark fringe is calculated. Radius of curvature is obtained fro the forula which is easily derived fro trignaetrical relationships. It is assued that the radius of curvature is large in coparison with the path difference. Figure 1. Newton s rings set up.

3 International Letters of Cheistry, Physics and Astronoy Vol Theory Fro the figure (1), r t (ab (1) ) ab () r t Fro trignaetry, ssuing ab to be very sall, 1 t tan ( ) (3) r R. ab ab R (4) where R is the radius of curvature of the plano convex lens Figure. Circle geoetry.

4 30 Volue 48 Experiental data, analysis and results Fro the condition for the foration of dark fringe (destructive interference) t (n 1) n t where t is the thickness of the air fil causing the foration of dark fringe λ is the wavelength of light used in the experient (5896 x ) For th dark fringe, n = t x (5) 10 Distance fro the centre to the th dark fringe in the experient is r =.90 x10-3 (6) Fro (), 3 ab (.9 10 ) ( ) Fro (3), tan ( ) radian Fro (4), Radius of curvature R Where as we have considered the th dark fringe for our calculations, any clearly visible fringe could be considered. 4. ALTERNATIVE METHOD TO FIND RADIUS OF CURVATURE This involves identifying a clearly visible dark fringe (say th dark fringe as in the previous case) and calculating the thickness of air fil creating the path difference causing the foration of dark fringe. The forula used is derived fro using geoetrical relationships. Fro figure (1) Siplification yields ( R t r R )

5 International Letters of Cheistry, Physics and Astronoy Vol t r Radius of curvature R t For th dark fringe, n =, Fro (5) & (6) t (7) 4.4x 10 Distance fro the centre to the th dark fringe in the experient is r =.90 x10-3 Substituting these paraeters in (7) R R (.9010 It ay be noted that the radius of curvature obtained fro the alternative ethods (1) & () are in close agreeent (0.96 & 0.95 respectively) with the result obtained through the general ethod (0.93). 3 ) 5. CONCLUSIONS Two alternative ethods to deterine the radius of curvature are presented. The results obtained are in close agreeent. The two proposed ethods are relatively easier as they involve easureent related to one fringe as copared to easureents related to 6 fringes in the general ethod. Based on the authors interactions with several student groups at undergraduate level, it ay be entioned that students while conducting these experiental ethods are able to develop an appreciation on how trigonoetry can be utilized to develop sipler alternative ethods. These alternative ethods ay be particularly useful in Industrial situations where radius of curvature any plano convex lenses are to deterined in a short duration of tie as these ethods involve lesser easureents (one fringe) and hence autoation is easier. Acknowledgeents The authors are deeply indebted to the authorities of CMR Institute of Technology, Bangalore for offering necessary laboratory and library facilities which resulted in this research work. References [1] Ajoy Ghatak, 1991, Optics,Tata Mcgraw Hill publication, 3 rd Edition, [] Chattopadhyay, 00, An advanced course in Practical Physics, Central Publication, 6 th Edition, 7 ( Received 17 February 0; accepted 4 February 0 )