Thermal Radiation Edited 4/24/18 by SA, JS, & DGH

Transcription

1 Thermal Radiatin Edited 4/24/18 by SA, JS, & DGH PURPOSE OF EXPERIMENT: T measure the energy/wavelength spectrum f a ht filament at different temperatures. Adjust fr the errrs inherent in the equipment used and generate true blackbdy radiatin curves fr each temperature. Cmpare yur results with thse predicted by Planck, Rayleigh-Jeans and Wein. OVERVIEW: A mnchrmatr will be cnstructed and used, in additin t a lead sulfide detectr and a cllectin f filters, t measure the intensity f light ver a range f frequencies. A light bulb filament will act as the cntinuus radiating surce. The mnchrmatr will direct a narrw wavelength interval f radiatin t the detectr where its intensity will be measured. The cllected intensities will be crrected fr a number f wavelength dependent variables and the resulting data will be used t create a wavelength dependent intensity spectrum. REFERENCES: Rhlf, pp ; Eisberg & Resnick, pp. 1-25; Tipler & Llewellyn, pp ; Enge, Wehr, and Richards, pp NOTES: This experiment uses fragile and expensive ptics. As a general rule, never tuch an ptical surface, particularly with yur skin. If nt remved within a few days, the ils in yur skin can cause permanent damage. This is a mre serius issue fr the reflective gratings which are expensive, fragile and very difficult t clean. If yu inadvertently tuch an ptical surface, please reprt it prmptly s it can be cleaned. Please keep fingers ff f all ptical surfaces. This experiment uses infrared radiatin. Sme substances, such as the ils frm yur skin, are transparent t visible light but nt t infrared; this is anther gd reasn nt t tuch the ptical surfaces. As an aside, this is why yu are nt suppsed t tuch the clear glass envelpe f a halgen bulb (prjectin bulb, autmbile headlight, etc.). Skin ils blck the exit f the IR radiatin and cause the bulb t verheat which distrts the shape f the glass envelpe and causes the filament t burn ut sner. APPARATUS: 1. Light Bulb - filament will act as the radiating surce. 2. Fan used as an ptical chpper 3. 2 Mirrrs 30 cm fcal length 4. Aperture t keep area f light hitting the grating a cnstant 5. Reflectin Grating lines per millimeter 6. Audi Amplifier t bst the detectrs signal 7. Oscillscpe - t read the signal strength nm Dide Laser - fr calibratin 9. Detectr Bx - Lead sulfide detectr plus a 5 psitin filter wheel: C = clsed, 1 = first filter, 2 = secnd filter, 3 = third filter and O = pen w/ n filter.

2 Nte: The lead sulfide detectrs are adversely affected by full spectrum rm light - even when turned ff. Please keep the filter wheel set t psitin C when the detectr is nt in use. Filters 1, 2 & 3 shuld prtect the detectr frm rm lights but the O psitin des nt. D nt turn the rm lights n when the filter is in the O psitin. Remember t cnsider the state f bth detectrs befre turning n the rm lights. PROCEDURE: 1. The rm temperature (300 K) resistance f the bulb is ± Ω. Befre turning n the bulb, use the same wires that will cnnect it t the pwer supply t cnnect it t a precisin multi-meter and measure its resistance. If using the HP multimeter, be sure t use the 2-wire inputs. Subtract this measured resistance frm the knwn rm temperature resistance f the bulb. Recrd this value; it is the resistance f the wires etc. that cnnect pwer t the filament. This value is a cnstant and shuld be subtracted frm all future resistance measurements. 2. T facilitate the precise angular measurements required in this lab, the rtating table that hlds the grating allws readings dwn t arcminutes. The table has tw scales, ne that ges frm and measures degrees and a Vernier that ges frm and measures arcminutes. T read the degrees, recrd the value clsely aligned with the 0 n the Vernier scale. In the case f Figure 1, that wuld be 28. Ntice that the 0 line reads slightly higher than 28. T find the arcminutes abve 28, find the line n the Vernier scale that aligns lines exactly with a line n the degree scale (the value n the degree scale des nt matter). In Figure 1, the 15 arcminutes mark aligns with a line n the degree scale. This means the ttal angle is Ntice that 45 the arcminutes mark als aligns with a line n the degree scale. T use this measurement yu wuld subtract 45 arcminutes frm 29, als giving Figure 1: A Vernier scale 3. Cnstruct and align the apparatus shwn in Figure 2, withut the aperture. The fcal length f mirrrs M1 & M2 is 30CM. The light surce and detectr shuld be placed precisely at the fci f these mirrrs. Keep the lng angle between mirrrs t abut 8. Nte: The setup clsest t the white bard shuld psitin M1 & M2 near the large pillar. The ther setup shuld be arranged in the ppsite rientatin.

3 Figure 2: Schematic f Mnchrmatr 4. Rtate the bulb in its hlder t rient the filament hrizntally. Set the bulb t ~9V. 5. With filter 1 in frnt f the detectr slit, adjust the light surce, mirrrs and grating t direct the 0 th rder reflectin int the detectr slit. If needed, adjust the distance between the light surce and M1 and the detectr and M2 t get a sharply fcused slit f light that just fits int the detectr slit. Be sure t lck dwn yur ptics. Recrd the angle f the grating; this is the 0 th rder psitin. 6. Rtate the grating cunter clckwise (CCW) and psitin the 0 th rder line back nt the slit in the light surce. Again recrd the angle f the grating. The difference in these tw values is half the angular separatin between M1 & M2. 7. Rtate the grating clckwise (CW) and psitin the 0 th rder back int the detectr slit. Withut changing the grating s psitin, turn ff the light surce and carefully remve the bulb assembly. Cautin, the light surce s aluminum husing will likely be ht. 8. Gently slide the laser pinter int the aluminum husing and psitin it s the red light (654nm) shines thrugh the slit. Fcused red light shuld appear at the detectr slit this is still the 0 th rder. Nw rtate the grating CW until a secnd fcused red light appears in the detectr slit this is the angular psitin f the 1 st rder at 654nm. Recrd this angle. 9. Use the angles recrded abve t calibrate yur mnchrmatr see belw.

4 Mnchrmatr Calibratin: The grating equatin is: nλ = d(sin θi sin θ) and fr the 0 th rder: θi = θ θ. Where n = the rder, λ = the wave length, d = the spacing between the grating lines, θi = the incident angle, θ = the diffracted angle, and θ = the diffracted angle fr the 0 th rder which is equal t θi. Figure 3.a: Definitin f θi and θ Figure 3.b: In the 0 th rder θi = θ = θ Nte: Angles nt t scale Δθ is defined as: Δθ = θi θ, which is equal t the scale reading at θi minus the scale reading at θ Therefre: θi = θ + Δθ and θ = θ Δθ This leads t: sinθ sinθ = sin( θ + θ ) sin( θ θ ) i = sinθ cs θ + csθ sin θ sinθ cs θ + csθ sin θ = 2csθ sin θ nλ = (2d csθ )sin θ Finding line width d: Nte: 1 Å = m, 1 nm = 10-9 and 1 μ =10-6 m Finding angle θ: The grating is 600 lines / mm s d 0.001m = = 1.67µ = 16,700Å 600 θ is the angle calculated in step 6. Use this t calculate the cnstant k belw t have an explicit expressin fr wavelength in terms f grating angle: 2 d csθ = k λ = sin θ k (n = 1)

5 10. Place the bulb assembly back int its husing with the filament in the hrizntal plane. Cnnect the pwer supply and set the vltage t ~9 V. Cnfirm that the 0 th rder psitin still directs the light int the detectr. Yu shuld nt have t make any adjustments. 11. Frm the 0 th rder psitin, rtate the grating 45 CW. Psitin the aperture t blck all light that is nt hitting the actual grating. Lck the aperture in psitin. Rtate the bulb assembly t rient the filament in the vertical plane. Cnfirm this light passes thrugh the aperture. If nt, rtate the filament 180 and check again. If yu cannt get filament light n the grating, ask the TA fr help. 12. Rtate the grading back t the 0 th rder and cnfirm the bright filament light passes thrugh the aperture and hits the grading. 13. With the gating at the 0 th rder and filter wheel set t 1; set the pwer supply t ~3V turn n the fan, detectr, amplifier, and scillscpe. Set the scillscpe vltage t 5V. Gently rtate the grating t identify the true angle fr the zerth rder. The signal will likely ver fill the screen. If this angle des nt match the ne fund in step 5, recrd this new angle as the true 0 th rder psitin. 14. Set the scillscpe time-scale t 200ms, the nise filter t 14KHz and add an RMS vltage display (use the measure buttn). Reduce the lamp vltage t ~2V. Set the filter wheel t C (clsed) and recrd the n light utput f the detectin system. This reading shuld be subtracted frm all future detectr readings. This nise value may vary with different vltage setting n the scillscpe. 15. Set the lamp vltage t ~11.5V. Use the current and vltage displayed n the pwer supply t calculate the filament resistance. Remember t subtract the cnstant fund in step 1. Use this resistance, the 300 K filament resistance and the tungsten resistivity chart belw t find the filament temperature at this vltage. 16. With the filter at 1, rtate the grating CW until a strng 1 st rder signal is bserved. When the signal ges frm very lw t strng, filter 1 has started transmitting and the 1 st rder ~0.5µm signal is entering the detectr see the filter graphs n the wiki under Equipment Manuals & References. Set the scillscpe vltage such that the signal cvers mst f the screen but des nt g ff the screen yu will need t adjust this thrughut yur data taking. 17. Set the grating angle t the beginning f the strng signal and recrd the vltage n the scpe and the angle f the grating. This is yur first data pint. 18. As the grating angle increases and the wavelengths get lnger, 0.5µm light frm the 2 nd rder will apprach the detectr slit. This light will pass thrugh F1 and wuld artificially increase the bserved vltage. F2 is used t prevent this light frm reaching the detectr. Use n λ = d(sinθ i sinθ ) and the filter graphs t determine when t change filters t prevent bserving light frm ther rders. Is the light frm the 3 rd r 4 th

6 rders a cncern? Is there a range between F1 & F2 r F2 & F3 that cannt prevent 2 nd r 3 rd rder light frm reaching the detectr? 19. Cntinue in the CW directin recrding the 1 st rder vltage every 2 frm 0.5µm t 2.3µm. Be sure t change filters as required. Recrd any changes made t the scpe gain during yur measurements. 20. Set the bulb vltage t ~5 vlts, recrd its resistance and take a secnd data set. 21. The vltages yu recrded cntain many errrs due t wavelength-dependent variables in emissivity, transmissin and refectin efficiency, electrical respnse, etc. T get a reliable vltage vs. wavelength plt, these variables must be accunted fr. 22. Befre attending next week s lab, create the Crrectin Table belw in excel and bring it t lab n a thumb drive. Fill in as many crrectin values and equatins as practical. This way yu will be able t tell if the data yu are taking is reasnable r if smething is wrng. There are digitized versins f the filter curves n the lab wiki that will make things much easier fr yu. INTENSITY CORRECTION TABLE Temp = Detectin system nise = Wavelength λ Measured Intensity I(λ) Emissivity Tungsten ET Reflectivity Mirrr 1 Rm1 Efficiency Grating GR Reflectivity Mirrr 2 Rm2 Transmissin Filter 1 F1 Transmissin Filter 2 F2 Transmissin Filter 3 F3 Respnse Detectr Dr Crrected Intensity Icr(λ) 23. Create a radiatin spectrum f the filament by pltting the crrected vltage vs. wavelength fr bth bulb temperatures. 24. Cmpare the tw spectra. Determine the effect f temperature n the psitin f the spectrum maxima and the intensity f the emitted radiatin. ANALYSIS: In yur analysis, include an INTENSITY CORRECTION TABLE as shwn abve. Plt bth spectra n the same graph. Include errr bars. Digitized versins f the three filter graphs can be dwnladed frm References & Resurces n the lab wiki.

7 DISCUSSION: Cmpare yur spectra with the theretical predictins f Wien 3 4 ( λ T = mk), Rayleigh-Jeans ( R = 2π ckt / λ ) and Planck max 2 5 ch / λkt ( Rλ = 2π c hλ /( e 1)). Use the spectra t determine the filament temperature. Discuss the errr in individual data pints. Estimate the accuracy f the value btained fr the temperature. Discuss pssible surces f systematic errrs in each analysis. λ R/R300K Temp Resistivity f Tungsten as a Functin f Temperature Resistivity R/R300K Temp Resistivity R/R300K Temp Resistivity R/R300K Temp Resistivity [K] µω cm [K] µω cm [K] µω cm [K] µω cm Nte: If a mre accurate resistivity at rm temperature is needed, the resistivity f Tungsten at 293 K is arund 5.3 µω cm. Surce: "Resistivity f Tungsten." Resistivity f Tungsten

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9 Grating Efficiency fr Randmly Plarized Light, Grating Blazed at 13º

10 See Equipment Manuals & References n the Wiki fr a digitized versin f this graph.

11 See Equipment Manuals & References n the Wiki fr a digitized versin f this graph.

12 See Equipment Manuals & References n the Wiki fr a digitized versin f this graph.

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