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Thermal Radiation Edited 5/3/16 by Stephen Albright, JS, & DGH PURPOSE OF EXPERIMENT: To measure the energy/wavelength spectrum of a hot filament at different temperatures. Adjust for the errors inherent in the equipment used and generate true blackbody radiation curves for each temperature. Compare your results with those predicted by Planck, Rayleigh-Jeans and Wein. OVERVIEW: A monochromator will be constructed and used, in addition to a lead sulfide detector and a collection of filters, to measure the intensity of light over a range of frequencies. A light bulb filament will act as the continuous radiating source. The monochromator will direct a narrow wavelength interval of radiation to the detector where its intensity will be measured. The collected intensities will be corrected for a number of wavelength dependent variables and the resulting data will be used to create a wavelength dependent intensity spectrum. REFERENCES: Rohlf, pp. 61-76; Eisberg & Resnick, pp. 1-25; Tipler & Llewellyn, pp. 123131; Enge, Wehr, and Richards, pp. 55-74. NOTES: This experiment uses fragile and expensive optics. As a general rule, never touch an optical surface, particularly with your skin. If not removed within a few days, the oils in your skin can cause permanent damage. This is a more serious issue for the reflective gratings which are expensive, fragile and very difficult to clean. If you inadvertently touch an optical surface, please report it promptly so it can be cleaned. Please keep fingers off of all optical surfaces. This experiment uses infrared radiation. Some substances, such as the oils from your skin, are transparent to visible light but not to infrared; this is another good reason not to touch the optical surfaces. As an aside, this is why you are not supposed to touch the clear glass envelope of a halogen bulb (projection bulb, automobile headlight, etc.). Skin oils block the exit of the IR radiation and cause the bulb to overheat which distorts the shape of the glass envelope and causes the filament to burn out sooner. APPARATUS: 1. 2. 3. 4. 5. 6. 7. 8. 9. Light Bulb - filament will act as the radiating source. Fan – used as an optical chopper 2 Mirrors – 30 cm focal length Aperture – to keep area of light hitting the grating a constant Reflection Grating - 600 lines per millimeter Audio Amplifier – to boost the detectors signal Multimeter and/or Oscilloscope - to read the signal strength 650nm Diode Laser - for calibration Detector Box - Lead sulfide detector plus a 5 position filter wheel: C = closed, 1 = first filter, 2 = second filter, 3 = third filter and O = open w/ no filter. Note: The lead sulfide detectors are adversely affected by full spectrum room light - even when turned off. Please keep the filter wheel set to position ‘C’ when the detector is not in use. Filters 1, 2 & 3 should protect the detector from room lights but do not turn the room lights on when the filter wheel is in the “O” position. Remember to consider the state of both detectors before turning on the room lights. PROCEDURE: 1. The room temperature (300˚K) resistance of the bulb is 0.810 0.002 . Before turning on the bulb, use the same wires that will connect it to the power supply to connect it to a precision multi-meter and measure its resistance. If using the HP multimeter, be sure to use the “2-wire” inputs. Subtract this measured resistance from the known room temperature resistance of the bulb. Record this value; it is the resistance of the wires etc. that connect power to the filament. This value is a constant and should be subtracted from all future resistance measurements. Additionally, students should check the resistance of the wires without the bulb to make sure that it is negligible. 2. To facilitate the precise angular measurements required in this lab, the rotating table that holds the grating allows readings down to arcminutes. The table has two scales, one that goes from 0-360 and measures degrees and a Vernier that goes from -60-0-60 and measures arcminutes. To read the degrees, record the value closely aligned with the 0 on the Vernier scale. In the case of Figure 1, that would be 28°. Notice that the 0 line reads slightly higher than 28°. To find the arcminutes above 28°, find the line on the Vernier scale that aligns lines exactly with a line on the degree scale (the value on the degree scale does not matter). In Figure 1, the 15 arcminutes mark aligns with a line on the degree scale. This means the total angle is 28° 15’. Notice that 45 the arcminutes mark also aligns with a line on the degree scale. To use this measurement you would subtract 45 arcminutes from 29°, also giving 28° 15’. Figure 1: A Vernier scale 3. Construct and align the apparatus shown in Figure 2, without the aperture. The focal length of mirrors M1 & M2 is 30CM. The light source and detector should be placed precisely at the foci of these mirrors. Keep the long angle between mirrors to about 4°. Figure 2: Schematic of Monochromator 4. Rotate the bulb in its holder to position the filament in the horizontal dimension. Set the bulb voltage to ~6V. 5. With filter 1 in front of the detector slit, open the grating door and rotate the grating to direct the 0th order reflection into the detector slit. Adjust the distance between the light source and M1 and the distance between M2 and the detector to get a sharply focused slit of light that just fits into the detector slit. Be sure to lock down your optics. Record the angle of the grating; this is the 0th order position. 6. Rotate the grating counter clockwise (CCW) and position the 0th order line back onto the slit in the light source. Again record the angle of the grating. The difference in these two values is half the angular separation between M1 & M2. 7. Rotate the grating clockwise (CW) and position the 0th order back into the detector slit. Do not change the grating position. Caution, the aluminum housing will likely be hot. Turn off the light source and remove it from its housing 8. Gently hold a laser pointer at the opening of the aluminum housing and position it so the red light (650nm 10) shines through the slit. Focused red light should appear at the detector slit – this is still the 0th order. Now rotate the grating CW until a second focused red light appears in the detector slit – this is the angular position of the 1st order at 650nm. Record this angle. 9. Use the angles recorded above to calibrate your monochromator – see below. Monochromator Calibration: The grating equation is: nλ = d(sin θi sin θ) and for the 0th order: θi = θ θo. Where n = the order, λ = the wave length, d = the spacing between the grating lines, θi = the incident angle, θ = the diffracted angle, and θo = the diffracted angle for the 0th order which is equal to θi. Figure 3.a: Definition of θi and θ Figure 3.b: In the 0th order θi = θ = θo Note: Angles not to scale Δθ is defined as: Δθ = θi θo, which is equal to the scale reading at θi minus the scale reading at θo Therefore: This leads to: θi = θo + Δθ and θ = θo Δθ sin i sin sin( o ) sin( o ) sin o cos cos o sin sin o cos cos o sin 2 cos o sin n (2d cos o ) sin Finding line width d: Note: 1 Å = 10-10 m, 1 nm = 10-9 and 1 μ =10-6 m The grating is 600 lines / mm so d 0.001m 1.67 16,700Å 600 Finding angle θo: θo is the angle calculated in step 6. Use this to calculate the constant k below to have an explicit expression for wavelength in terms of grating angle: 2d cos o k k sin (n = 1) 10. Place the bulb assembly back into its housing with the filament in the horizontal plane. Connect the power supply and set the voltage to ~6 V. Confirm that the 0th order position still directs the light into the detector. 11. From the 0th order position, rotate the grating CW through 55o. Position the aperture to block all light except that which is hitting the actual grating. Lock the aperture in position. 12. Rotate the bulb assembly to position the filament in the vertical plane. If the filament light is not passing through the aperture, rotate the filament 180o. If you cannot get filament light on the grating, ask the TA for help. 13. Set the gating back to the 0th order position and turn the fan on. 14. With filter 1 set in position, turn on the detector, amplifier, and oscilloscope. To measure the voltage on the oscilloscope, use a 200ms time-scale and use the “measure” button to add an RMS voltage readout of the signal. Confirm that the 0th order angle, found in step 6, provides the maximum signal. If a small angular change gives the maximum signal, record this angle as the true 0th order position. 15. Temporarily reduce the lamp voltage to ~2V. Set the filter wheel to C (closed) and record the no light output of the detection system. This reading should be subtracted from all future detector readings. 16. Set the lamp voltage to ~11.5V. Use the current and voltage displayed on the power supply to calculate the filament resistance. Remember to subtract the constant found in step 1. Use this resistance, the 300˚K filament resistance and the tungsten resistivity chart below to find the filament temperature at this voltage. 17. Set the filter to 1 and rotate the grating CW until a strong 1st order signal is observed. When the signal goes from very low to strong, filter 1 has started transmitting and the 1st order ~0.5m signal is entering the detector – see the filter graphs on the wiki under Equipment Manuals & References. 18. Set the grating angle to the beginning of the strong signal and record the voltage on the scope and the angle of the grating table. This is your first data point. 19. Continue in the CW direction recording the 1st order voltage every 2° from 0.5m to 2.3m. Record any changes made to the scope gain during your measurements. 20. As the grating angle increases and the wavelengths get longer, 0.5m light from the 2nd order will approach the detector slit. This light will pass through F1 and would artificially increase the observed voltage. F2 is used to prevent this light from reaching the detector. Use n d (sin i sin ) and the filter graphs to determine when to change filters to prevent observing light form other orders. Is the light from the 3rd or 4th orders a concern? Is there a range between F1 & F2 or F2 & F3 that cannot prevent 2nd or 3rd order light from reaching the detector? 21. Set the bulb voltage to ~4 volts, record its resistance and take a second data set. 22. The voltages you recorded contain many errors due to wavelength-dependent variables in emissivity, transmission and refection efficiency, electrical response, etc. To get a reliable voltage vs. wavelength plot, these variables must be accounted for. 23. Before attending next week’s lab, create the Correction Table below in excel and bring it to lab on a thumb drive. Fill in as many correction values and equations as practical. This way you will be able to tell if the data you are taking is reasonable or if something is wrong. There are digitized versions of the filter curves on the lab wiki that will make things much easier for you. INTENSITY CORRECTION TABLE Corrected Intensity Icor(λ) Response Detector Dr Transmission Filter 3 F3 Transmission Filter 2 F2 Transmission Filter 1 F1 Reflectivity Mirror 2 Rm2 Efficiency Grating GR Reflectivity Mirror 1 Rm1 Emissivity Tungsten ET Measured Intensity I(λ) Wavelength λ Temp = _______ Detection system noise = _______ 24. Create a radiation spectrum of the filament by plotting the corrected voltage vs. wavelength for both bulb temperatures. 25. Compare the two spectra. Determine the effect of temperature on the position of the spectrum maxima and the intensity of the emitted radiation. ANALYSIS: In your analysis, include an INTENSITY CORRECTION TABLE as shown above. Plot both spectra on the same graph. Include error bars. Digitized versions of the three filter graphs can be downloaded from “References & Resources” on the lab wiki. DISCUSSION: Compare (max T 2.90 10 3 mK ) , your spectra with Rayleigh-Jeans the theoretical predictions and ( R 2 ckT / 4 ) of Wien Planck ( R 2 c 2 h5 /( e ch / kT 1)) . Use the spectra to determine the filament temperature. Discuss the error in individual data points. Estimate the accuracy of the value obtained for the temperature. Discuss possible sources of systematic errors in each analysis. Resistivity of Tungsten as a Function of Temperature R/R300K Temp Resistivity R/R300K Temp Resistivity R/R300K Temp Resistivity R/R300K Temp Resistivity 1.0 1.43 1.87 2.34 2.85 3.36 3.88 4.41 4.95 [K] 300 400 500 600 700 800 900 1000 1100 cm 5.65 8.06 10.56 13.23 16.09 19.00 21.94 24.93 27.94 5.48 6.03 6.58 7.14 7.71 8.28 8.86 9.44 10.03 [K] 1200 1300 1400 1500 1600 1700 1800 1900 2000 cm 30.98 34.08 37.19 40.36 43.55 46.78 50.05 53.35 56.67 10.63 11.24 11.84 12.46 13.08 13.72 14.34 14.99 15.63 [K] 2100 2200 2300 2400 2500 2600 2700 2800 2900 cm 60.06 63.48 66.91 70.39 73.91 77.49 81.04 84.70 88.33 16.29 16.95 17.62 18.28 18.97 19.66 26.35 [K] 3000 3100 3200 3300 3400 3500 3600 cm 92.04 95.76 99.54 103.3 107.2 111.1 115.0 Note: If a more accurate resistivity at room temperature is needed, the resistivity of Tungsten at 293 K is around 5.3 µΩ cm. Source: "Resistivity of Tungsten." Resistivity of Tungsten. 2004. http://hypertextbook.com/facts/2004/DeannaStewart.shtml Grating Efficiency for Randomly Polarized Light, Grating Blazed at 13º See “Equipment Manuals & References” on the Wiki for a digitized version of this graph. See “Equipment Manuals & References” on the Wiki for a digitized version of this graph. See “Equipment Manuals & References” on the Wiki for a digitized version of this graph.