8. Wavelength measurement with a grating spectrometer

Transcription

1 Spm 8. Wavelength meaurement with a grating pectrometer 8.1 Introuction A very exact examination of the chemical compoition of a ubtance can be unertaken by analying the electromagnetic raiation it emit or aborb when light hine through it. The electron of an atom can only occupy tate of certain, icrete energie, wherea the pectrum of allowe tate i characteritic for a given kin of atom or molecule. The wavelength of electromagnetic raiation which i being emitte or aborbe when a tranition from one to another tate happen i etermine by the energy ifference of the initial an final tate an i therefore quantie a well (quantization = only icrete value). Thi lea to the rie of a line pectrum which i characteritic for the ort of examine atom or molecule. Often even light trace of a ubtance are ufficient to generate verifiable pectral line. In thi lab coure, the line pectrum of a helium lamp hall be examine in the range of viible light an the wavelength of the occurring pectral line hall be etermine with the help of interference on a fine graticule. A econ metho for the ecompoition of viible light into it pectral color, namely the refraction of light inie of a cuneiform prim, i being oberve in the lab coure Spk. Interference phenomena with viible light are alo examine in the lab coure I an M. 8. Theoretical part The emergence of an interference pattern at a ingle lit i being icue extenively in the theoretical part of the lab coure I. When a plain wave hit a lit perpenicularly, the Huygen- Frenel principle tell u, that every point in the lit can be een a the ource of a pherical wave an all thee pherical wave are in phae with each other in the lit plane. If the lit with i in the ame orer of magnitue a the wavelength λ = π/k of the light, the uperpoition of thoe pherical wave lea to the raie of an interference pattern. At a point P, which i locate at a itance r 0 from the lit at an angle of θ to the ymmetric axi, the cumulative wave from the ingle lit a up to 1

2 8. Wavelength meaurement with a grating pectrometer at an intenity of u lit ( ) = in k in θ ( ) k k in θ co in θ + ωt kr 0 I lit (θ) in k in θ k in θ (8.1) (8.) The overall picture for a graticule which conit of N parallel lit of with reult from the uperpoition of the wave pattern of all ingle lit. If the itance r 0 of the repective point to the grating i very large compare to the wiening of the grating, one can aume the obervation angle θ to be the ame for all lit of the grating (ee Fig. 8.1). If i the itance of two neighbouring lit, then the wave of thoe two lit are iplace againt each other in the point P by a phae of k in θ. Therefore, the over-all wave in P become N in k u grating (θ) = in θ ( ) k k n=0 in θ co in θ + ωt kr 0 k n in θ an after the accomplihment of the ummation an quaring it follow after ome naty calculation (ee lecture cript) that the intenity of the wave amount to in k I grating (θ) in θ in N k in θ k in θ ( ) in k in θ (8.4) The intenity behaviour i chematically epicte in Fig. 8.. So-calle major maxima appear for in θ = n λ where n = 0, 1,,... (8.5) an in-between two major maxima lie N a intenity minima an N ub maxima. The amplitue of the major maxima i moulate with the interference pattern of a ingle lit. In (8.3) n = 0 1 Towar point P 3 inθ N 1 θ Figure 8.1: Interference at the grating. Laboratory manual for Phyic Major - PHY11/1

3 8.. THEORETICAL PART 3 the figure the quare root of the intenity i being hown in orer to enhance the viibility of the trongly uppree ub maxima next to the major maxima. I Firt orer maximum 3λ λ λ λ λ 3λ 0 in θ Figure 8.: Interference pattern at the grating. For a known lit iplacement one can etermine the wavelength λ from the location of the major maxima. A grating uit better for a wavelength meaurement than a ingle lit, ince the major maxima are much better reolve than the intenity maxima of a ingle lit. The itance of two major maxima from a grating account for λ, wherea the with of a major maxima i efine by the itance λ N between the two neighbouring minima. Thu, the major maxima become harper if they re eparate better from each other, which happen when we increae the number of lit N in the grating. For a irect comparion, the interference pattern for a ingle lit, a ouble lit an a grating are hown in Fig. 8.3 one more time. Single lit Double lit = 3.5 N lit N = 8, =.5 I I I 0 in θ λ in θ λ in θ N λ λ λ Figure 8.3: Interference pattern of a ingle lit, a ouble lit an a grating. Laboratory manual for Phyic Major - PHY11/1

4 4 8. Wavelength meaurement with a grating pectrometer 8.3 Experimental part In thi experiment you hall etermine the wavelength of the pectral line of a helium lamp in the range of viible light with the ai of a grating pectrometer. In total, one can itinguih eight itinct line: Colour re re yellow green green blue-green blue purple Intenity very weak meium intene weak intene meium meium intene Experimental et-up The et-up i hown in Fig S Collimator L 1 Grating table He Lamp L θ Telecope Ocular L 3 Groun gla with crohair Figure 8.4: Grating pectrometer. The collimator an the telecope erve the purpoe to realie the approximation taken in the erivation of Equ. 8.5 for an incoming plane wave an a oberving point which lie far away from the grating. The He-lamp lighten a narrow lit which lie in the focal plane of the collimator len L1. Therefore, the light arrive jut about parallel to the optical axi at the grating which correpon to a plane wave front. The len L oe focu the incoming parallel wave from the grating for it focal plane, where the interference pattern can be oberve on matt creen with the help of the ocular L 3. The matt creen i provie with a reticle, which, by turning the telecope aroun the rotation axi of the pectrometer, i being aligne to be meaure. The viewing angle θ can then be rea off on a vernier gauge with an accuracy of an arc minute. Calibration of the pectrometer Before the actual meaurement, the grating pectrometer ha to be calibrate in uch a way that the optical axe of the collimator an the telecope run through the rotation axi of the pectrometer an tan perpenicular to thi axi. Laboratory manual for Phyic Major - PHY11/1

5 8.3. EXPERIMENTAL PART 5 Replace the grating with a plane parallel mirror an the meaurement ocular with a Gauian telecope ocular. Ajut the ocular uch that, both, the hair cro an it mirror image are iplaye harply at the ame time. Align the hair cro an it mirror image by turning the grating table an inclining the table plane. Check, whether the telecope axi an the turning axi of the pectrometer tan perpenicular to each other by turning the grating table by 180 an again oberving the hair cro an it mirror image. If neceary, align them, where you perform about half of the neceary ajutment at the telecope an the other half at the grating table. Repeat thi proceure until the hair cro an it mirror image align in both etting. Remove the mirror an replace the Gauian ocular with the meaurement ocular. Lock the collimator lit in a vertical poition. Ajut the collimator len uch that the image of the lit an the hair cro appear harply in the in the ocular at the ame time. Incline the collimator uch that the image of the lit appear ymmetrically to the hair cro. Attach the grating on the grating table. The pectrometer i now reay for the meaurement. Meaurement an evaluation For each of the eight pectral line, meaure the angle of the maximum of firt orer. Do it firt on one ie of the not eflecte ray, then on the other ie of the not eflecte ray. Align the hair cro with the interference maximum an rea off the oberving angle. Alo, etermine the oberving angle for the not eflecte ray. Repeat the whole meaurement a econ time an take the average value of your meaurement. Calculate the wavelength of the eight pectral line after Equ The value of the grating contant i eclare at the et-up ie. Repeat the meaurement for one of the brighter line an aitional three time on both ie of the not eflecte ray. From all the meaurement you performe for thi particular line, etermine the uncertainty m θ. Determine the uncertainty on the wavelength meaurement uing the propagation of uncertainty: m λ = λ (m ) + ( ) min θ (in θ) where m in θ = m θ in θ θ = m θ co θ (8.6) Laboratory manual for Phyic Major - PHY11/1