Bnibling/Acoustic Lab

Spectroscopy

Barrett Nibling, Travis Nokes, Kurt Strovink

November 6th, 2007

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Procedure

Schematic of Spectroscopy Apparatus

Results

Helium Results

Helium, d=1/600mm, m=1

Color	θdiff (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	???

Error Analysis

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

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

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

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_diff 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.