Page 1 : ‘FABRY-PEROT INTERFEROMETER AND ETALON —, , ‘i . $ \, The Fabry-Perot interferometer is a high resolving power instrument, which makes Ue of, ‘fringes of equal inclination’, produced by the transmitted light after multiple reflections inan a :, , film between two parallel highly reflecting glass plates., , , , , , , , , The interferometer consists of two, optically plane glass plates A and B with their, inner surfaces silvered, and placed, accurately parallel to each other. Screws are, provided to secure parallelism if disturbed., This system is difficult to manufacture and, is no more in use. Instead an etalon which is, much more easily manufactured is used. The, etalon consists of two semi-silvered plates, rigidly held parallel at a fixed distance apart., The reflectance of the two surfaces can be, , as high as 90 to 99.9%. Although both idee ‘5s, reflected and transmitted beams interfere Fabry-Perot Interferometer., , , , , , , Scanned with CamScanner

Page 2 : . . ee, bry-Perot interferometer is usually used i, in the transmissi, Ssive mode,, , spor, the Fe : :, , ; ochromatic light and ., ne source 0 monochrom ight and L, a conve:, , x gis 08 8 parallel. An incident ray suffers a abies, , ic, Eh makes ie ‘vo silvered surfaces, as shown in Fig.15.35. At each, , sie a ransmitte, , (not shown in Fig, 15.35), er of internal Teflections, , ‘ai Teflectio :, d also. Thus, each incident ray produces a group of ork ae, and parallel,, , 00 ht ; nt path di tw tw, \ ted pays with a ate toa vain ie f al ere Where heated, gilt ose rays In its focal plane whe i ee, : re they interfere, H, » Hence the rays, , be be ing f the source produce an interference pattern o;, , a oints 0 n a screen placed in th, , 1 gom all? n the focal plane of, \ ffo', , EL, \ 15-1, , TION OF FRINGES, , 4. FORMA, ° aration between the two silvered surf: i, Letdbe the sep’ f surfaces and 0 the inclinati ‘i, | to the plates. The path difference between any two sont aiaiie,, rays, , aywilh the be ident ray is 2d cos 0 iti, \ responding to the mes y is 2d cos 8. The condition for these rays to produce maximum, , comtest, intensity 'S, 2d cos 8=mi, t yerem is an integer. The locus of points in the source, which give rays of constant inclination, 0 is, with an extended source, the interference pattern consists of a system of bright, , acirole. Hence, :, concenttic rings on a dark background, each ring corresponding to a particular value of 6., , 15.12.2. DETERMINATION OF WAVELENGTH, , When the reflecting surfaces A and B of the interferometer are adjusted exactly parallel,, , , circular fringes are obtained. Let m be the order of the bright fringe at the centre of the fringe, system. As at the centre 6 = 0, we have, j 2t =md, Ifthe movable plate is moved a distance 1/2, 2t changes by And hence a bright fringe of the, vable plate is moved from the position x, to x, and the, , next order appears at the centre. If the mo, number of fringes appearing at the centre during this movement is N, then, , When, Z i 2078) (15.77), | Measuring x,,x, and N, we can determine the value of A., ' 15.12.3, MEASUREMENT OF DIFFERENCE IN WAVELENGTH tne, i dD, lines in, The light emitted by a source may consist of two or more wavelengths, as D, and}; i, vse of sodium. Separate Ringe patterns corresponding to the two wavelengths are not pete =, meter is not suitable to study the fine struct, , Jength produces its, , r, cach wave, t interferometer, , Michelson interferometer. Hence, Michelson interfero', ry-Pero', , pepeatal lines. On the other hand, in Fabry-Perot in, is Sia pattern and the patterns are separated from each other., llable to study the fine structure of spe i atin, Close Difference in wavelengths can be found using coin, interfer roneths in the incident light. Let us assu ol, Oe are brought into contact. Then the rings ie , a, curs € plate is slowly moved away such that the ring sy tome ave (0 1, : Then the rings due to A, are half way betwe a cal a, , ewe j, €n the plates when maximum disco, , terferomete!, Therefore, Fab, , ethod. Let A, and A, betwo very, , two plates of the, artially. Then the, , ‘Scanned with CamScanner, , 2H = my = (™ +4)2)

Page 3 : or m (4 =p) =Ag/2, , Ag, m =—— >, 1" 2(A, -A2), ‘ . dg x, Using the value of m, in equ.(15 .78), we get 24, = 2(%—%n) 1, «Agha Mmetin, Mae ag dg, , (since AyAy =Amean? AS Ay — Ay is very small)., , When the separation between the plates is further increased, the ring systems Coincide again, urs once again. If ¢, is the thickness now,, , and then separate out and maximum discordance occ, 2t, = mA, = (m, +3.), From equ.(15.81) and (15.78), we get, Aly =f) = (my — Mm Jay = (mm, —M, )Ag + Aq, , , , Ay, My —m,) =, ot (m -m)=578—, Using the above expression into equ.(15.82), we obtain, Av, 2(t,-1,)=—2, (4, -Ag), 2, or . ay - A = Fah = mean, 2(t)-4) 2(t, ~1), , (15.75), , (15.89 |, , (15.81), , (15.80), , (15:83) |, , = — SS, , , , Scanned with CamScanner