Badboys/template

Gamma Ray Attenuation

Barrett Nibling, Adolfo Gomez, Micheal Bouchey

February 6, 2008

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Abstract

abstract here

List of Figures

• figure 1

• figure 2

• figures 3

Introduction

intro here

Theory

Theory here

Example Math:

$Sin(\theta_{inc})+ Sin(\theta_{diff})=\frac{m \lambda}{d}$,

$Sin(\theta_{diff})=\frac{m \lambda}{d}.$

$\lambda = \frac{d Sin(\theta_{diff})}{m}.$

Procedure

procedure here

Example Image:

Schematic of Spectroscopy Apparatus

Results

Data here

Results 1

Example Table

The First Order Spectrum:

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

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

conclusion here

References

[1]

[2]