Bnibling/Acoustic Lab

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Revision as of 02:46, 4 December 2007

Spectroscopy

Barrett Nibling, Travis Nokes, Kurt Strovink

November 6th, 2007

Abstract

List of Figures

Introduction

Theory

Procedure

Schematic of Spectroscopy Apparatus

Results

Helium Results

The following tables and graphs are the results acquired from the Helium Spectroscopy. All published values are from [2].

The First Order Spectrum:

Helium, d=1/600mm, m=1
Color	$θ d i f f$ (degrees)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Purple	15.6	448.0	$\pm$ 2.0	447.148
Teal	16.4	470.3	$\pm$ 2.0	471.314
Green	17.2	492.6	$\pm$ 2.0	492.193
Green	17.5	500.9	$\pm$ 2.0	501.567
Yellow//Orange	20.7	588.8	$\pm$ 2.0	587.562
Red	23.6	666.9	$\pm$ 2.0	667.815
Dim Red	25.1	706.7	$\pm$ 1.9	???

The graph above is a comparision between the wavelength calculated using the working equation and the published values, with all values when the error bars.

The following is the first order spectrum of Helium using a 300mm grating

Helium, d=1/300mm, m=1
Color	$θ d i f f$ (degrees)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Purple	7.7	446.4	$\pm$ 4.1	447.148
Teal	8.1	469.4	$\pm$ 4.1	471.314
Green	8.5	492.5	$\pm$ 4.1	492.193
Green	8.6	498.2	$\pm$ 4.1	501.567
Yellow//Orange	10.2	590.0	$\pm$ 4.1	587.562
Red	11.5	664.2	$\pm$ 4.1	667.815
Dim Red	12.2	704.0	$\pm$ 4.1	???

Due to the higher amount of error associated with the 300mm grating compared to the 600mm grating, about twice as much, we opted to discontinue any further data collection using the 300mm and stuck with the 600mm for the remainder of the lab.

The Second Order Spectrum:

Helium, d=1/600mm, m=2
Color	$θ d i f f$ (degrees)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Purple	32.5	447.5	$\pm$ .95	447.148
Teal	34.4	470.6	$\pm$ .94	471.314
Green	36.4	491.6	$\pm$ .94	492.193
Green	37.0	501.3	$\pm$ .93	501.567
Yellow//Orange	44.9	588.0	$\pm$ .89	587.562
Red	53.3	667.9	$\pm$ .85	667.815

In the second order domain, the error is about half of the error in the first order. Even so, all the values when compared to published values are within the error bars.

Sodium Results

The following tables are the result acquired from the Sodium Spectroscopy. Again, the published results are from reference [2].

The First Order Spectrum: In the first order spectrum there are many lines and using the data from the Helium portion of the lab determined that the Sodium has Helium contamination. By substracting all the known Helium lines, all that was left is a bright orange line. By focusing the slit, it was determined to actually be 2 orange lines, this can be seen better in the second order spectrum. Due to the proximity of the lines, less than .1 degrees apart, one measurement was taken and the published values were averaged.

Sodium, d=1/600mm, m=1
Color	$θ d i f f$ (º)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Orange	20.7	588.8	$\pm$ 1.99	589.294

Second Order Spectrum: In the second order, all the contamination was removed and only the oranges lines were seen.

Sodium, d=1/600mm, m=2
Color	$θ d i f f$ (degrees)	$λ$ (nm)	Error (nm)	Published $λ$ (nm)
Orange	46	594.14	$\pm$ .89	589.294

Error Analysis

For the error analysis, there are two variable associated with an error, $θ d$ and $θ i$ .

The partial errors for each of the variable are calculated from the formulas

$\frac{\delta \lambda}{\delta \theta_{d}}=\frac{d}{m}Cos(\theta_{d})Sin({\delta \theta_{d}}),$

and,

$\frac{\delta \lambda}{\delta \theta_{i}}=\frac{d}{m}Cos(\theta_{i}) Sin({\delta \theta_{i}}).$

Then the total error is the sum of the two partial derivatives added in quadrature,

$\delta \lambda=\frac{d}{m} \sqrt{(\frac{\delta \lambda}{\delta \theta_{i}})^{2}+(\frac{\delta \lambda}{\delta \theta_{d}})^{2}}.$

The values for $δθ d$ and $δθ i$ used are half the value of the smallest unit of measure on the device, .05 degrees.

Conclusion

The emission spectrum for the sodium and helium sources is determined accurately; the error is under 1% and published values fall within that error. The sole exception, the error present in the second order sodium band, is considered to be due to human error during data collection rather than any deviation from the model. The symmetry about $θ d i f f$ allows each measurement to be confirmed, resulting in confidence in these results.

References

[1]Kowalski et al., Spectroscopy, 2007.

[2]Jenkins, F A and White, H E , Fundamentals of Optics, 4E, McGraw-Hill, 1976.

@@ Line 16: / Line 16: @@
 == Procedure ==
-As shown below, a collimator is placed in front of the helium/sodium lamp, focusing the light into one beam.  One of the two (300/mm, 600/mm) diffraction gratings is positioned level with the light source and perpendicular to the axis of the beam.  A  telescope is positioned level with the observed beam.  When properly arranged, the light seen through the telescope is observed at 0º, as read on the Vernier scale goniometer.
-The angle of the telescope eyepiece changes with reference to this 0º starting point as it is moved along the scale. This allows the observer to measure the angle at which the maxima occur for each color emitted. The location of each color band is measured and recorded.  The diffraction grating is exchanged and the measurements repeated for m = 1,2.

Bnibling/Acoustic Lab

Revision as of 02:46, 4 December 2007

Contents

Abstract

List of Figures

Introduction

Theory

Procedure

Results

Helium Results

Sodium Results

Error Analysis

Conclusion

References

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