3. Newton s Rings. Background. Aim of the experiment. Apparatus required. Theory. Date : Newton s Rings

Transcription

1 ate : Newto s igs 3. Newto s igs Backgroud Coheret light Phase relatioship Path differece Iterferece i thi fil Newto s rig apparatus Ai of the experiet To study the foratio of Newto s rigs i the air-fil i betwee a plao-covex les ad a glass plate usig early oochroatic light fro a sodiu-source ad hece to deterie the radius of curvature of the plao-covex les. Apparatus required A early oochroatic source of light (source of sodiu light) A plao-covex les A optically flat glass plates A covex les A travelig icroscope Theory Fig.. Newto s rigs Whe a parallel bea of oochroatic light is icidet orally o a cobiatio of a plao-covex les L ad a glass plate G, as show i Fig., a part of each icidet ray is reflected fro the lower surface of the les, ad a part, after refractio through the air fil betwee the les ad the plate, is reflected back fro the plate surface. These two reflected rays are coheret, 3

2 Newto s igs hece they will iterfere ad produce a syste of alterate dark ad bright rigs with the poit of cotact betwee the les ad the plate as the ceter. These rigs are kow as Newto s rig. For a oral icidece of oochroatic light, the path differece betwee the reflected rays (see Fig.) is very early equal to t where ad t are the refractive idex ad thickess of the air-fil respectively. The fact that the wave is reflected fro air to glass surface itroduces a phase shift of. Therefore, for bright frige t ; = 0,,,3 () ad for dark frige t ; = 0,,,3 () For -th (bright or dark) rig (see Fig. ), we also have t (3) 4 where = the diaeter of the -th rig ad = the radius of curvature of the lower surface of the plao-covex les. O eglectig t, equatio (3) reduces to = 8t (4) Fro equatios () ad (4), we get, λ 4, for -th bright rig (5) μ λ 4, μ for (+)-th bright rig (6) Siilarly, fro equatios () ad (4), we obtai 4, for -th dark rig (7) 4( ), for (+)-th dark rig (8) Thus for bright as well as dark rigs, we obtai Sice = for air-fil, above equatio gives μ 4λ 4λ (9) (0) 33

3 Newto s igs Procedure. Level the travelig icroscope with its axis vertical. Arrage the set-up as show i Fig. ad focus the icroscope o the air-fil. Newto s igs will be clearly see.. Adjust the glass plate G for axiu visibility of the poit of cotact of les L with the glass plate G ad hece for axiu visibility of Newto s igs. I this orietatio, G is at 45 0 to the icidet bea of light. 3. Move the icroscope to the right of the cetral dark spot (say order, this is because the cetral rig is ofte broad ad ay ot ecessarily will be zero order) ad set it o the extree teth (+0 th order) distict bright rig so that the cross-wire perpedicular to the directio of oveet of the icroscope passes through the bright rig ad is tagetial to it. ecord the icroscope positio fro the horizotal scale alog with its uber with bright rig aroud the cetral dark spot as the first bright rig. Move the icroscope to left ad record the positio of the ext bright rig. epeat it till you reach to the teth bright rig o the left. Fro these easureets, evaluate the diaeters of differet rigs. epeat these easureets for icroscope oveet fro left to right ad evaluate the diaeters of differet rigs. eterie the average diaeters of differet rigs. 34

4 Observatios Newto s igs Verier costat for the horizotal scale of the icroscope (Least Cout) : Table Measureets of the diaeter of the rig Microscope readigs (c) o the ig No. () Mai Scale Left ( ) ight ( ) Verier Total Mai scale Verier Total iaeter + = - (c) (c ) (c )

5 Newto s igs Calculatio ad esults Plot a graph betwee vs - Table Calculatio of radius of curvature,, fro the graph (c ) fro graph - (c) ( ) 4( )λ (c) 36

6 Newto s igs 37 Estiate error i The radius of curvature is calculated fro Equatio (3), viz. )λ - 4( Sice ad are oly easured, the axiu proportioal error i is give by δ δ = ) ( ) ( Sice or is easured by takig the differece betwee the two readigs of a scale provided with a verier, the axiu error i easurig each of these quatities is twice the verier costat i.e. v.c. Therefore, c v. Hece, ) (. 4 ) (. 4 v c v c

7 Newto s igs iscussio (i) The Newto s rig experiet ca be also used to fid the wavelegth of a oochroatic light. I this case, the radius of curvature of the covex surface of the give les is supplied or is deteried otherwise. By eployig sodiu light whose ea wavelegth is 5893Å, ca be deteried fro Eq.(3), as i the preset experiet. The the sae equatio ca be used to fid the wavelegth of ay other give oochroatic light. 38

8 Newto s igs (ii) is calculated fro Eq. (0). A error i the actual rig uber + does ot affect the result. (iii) Sice the first few rigs ear the ceter are defored, they ust be avoided while takig readigs for the rigs. (iv) Care ust be take ot to disturb the les ad glass plate cobiatio i ay way durig the experiet. Questios. I the Newto s rig experiet, how does iterferece occur?. Where have the friges fored? 3. Why are the friges circular? 4. Are all rigs equispaced? 5. Why is a exteded source used i this experiet? 6. What will happe if a poit source or a illuiated slit is used istead of the exteded source? 7. I place of les, if a wedge shaped fil fored by two glass plates is supplied to you, will you be able to observe Newto s rig? Why? 8. How is the cetral spot i your experiet, bright or dark? Why? 9. Istead of reflected rays, if you look at trasitted rays, what do you expect to observe? 0. What happes with the cetral spot whe a liquid of refractive idex greater tha that of the les ad less that that of the glass plate is itroduced betwee the les ad the glass plate?. Is it possible to deterie the refractive idex of the liquid by this experiet?. What would happe to the rig if the space betwee les ad the plate is filled with a liquid of refractive idex? 3. What do you expect to see i the icroscope if you use a white light source? 4. What is the differece betwee bipris friges ad Newto s rig friges? 5. O which factors does the diaeter of a rig deped? 6. What would happe if a glass plate is replaced by a plae irror? 7. Why should a les of large radius of curvature be used i this experiet? 8. Is it desirable to easure the radius of curvature of the give les by a spheroeter i the usual way? 9. What do you uderstad by (a) friges of equal thickess (b) friges of equal icliatio ad (c) friges of equal chroatic order. 0. How does the sodiu source, which you are usig i your experiet work? efereces. Fudaetal of Optics by F. Jekis ad H. White 535 JEN/F. Optics by A.Ghatak 535 GHA/O 3. Optics by E. Hecht 535 HEC/O 39

9 Newto s igs Graph : Newto s igs 40