Calculating Error In Wavelength

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SUMMARY

The discussion focuses on calculating the error in wavelength using the formula \(\lambda = d \cdot \sin(x)\), where \(d\) is the slit size of \(\frac{1}{600000}\) meters and \(x\) represents measured angles in degrees. The error in wavelength, \(\delta\lambda\), is derived as \(\delta\lambda = \frac{|\cos(x)| \cdot \delta x}{600000}\) with \(\delta x\) set at 0.1 degrees. Each angle produces a different error, and it is common practice to calculate the error for a central angle and apply it uniformly across all measurements.

PREREQUISITES
  • Understanding of trigonometric functions, particularly sine and cosine.
  • Familiarity with error propagation in measurements.
  • Knowledge of basic physics principles related to wave mechanics.
  • Ability to perform calculations involving angles in degrees.
NEXT STEPS
  • Study the principles of error propagation in physics experiments.
  • Learn about the significance of using central values in error estimation.
  • Explore the impact of varying slit sizes on wavelength calculations.
  • Investigate the relationship between angle measurements and wavelength in diffraction experiments.
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Students in physics, particularly those working on optics and wave mechanics, as well as educators teaching error analysis in experimental physics.

azntoon
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Homework Statement



I am unsure whether I am calculating the error correctly for the wavelength
given that x=14.3,15.3,16.2,17.1,23.3 all in degrees

Homework Equations



\lambda=d*Sin(x)

where d is my slit size in meters \frac {1}{600000}
x=measured angle
\delta x= 0.1 degrees

The Attempt at a Solution



\delta\lambda= \frac {|Cos(x)|\delta x}{600000}

Now with my given x's they would produce a different error each time is that right or how do I get an over all error?
 
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Yes, that is the correct expression for the error and it will be different for each angle. Error is an estimate, so it is quite common to just work it out for a middle value and apply that same size error bar to all the points.
 
Thank you very Much
 

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