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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 ~0.5m 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 0.5m to
2.3m. Record any changes made to the scope gain during your measurements.
20. As the grating angle increases and the wavelengths get longer, 0.5m 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 h5 /( 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.