Calculating the overall uncertainty of my measurements

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SUMMARY

This discussion focuses on calculating the overall uncertainty in measurements taken during an experiment to determine the refractive index of sugar solutions. The user measured lengths with an estimated uncertainty of +/- 0.025 cm and applied trigonometric functions to derive a final expression. The key conclusion is that uncertainty can be propagated through trigonometric operations using standard rules for addition, subtraction, multiplication, and division. Additionally, the user suggests a method for determining maximum and minimum values to estimate uncertainty in the final result.

PREREQUISITES
  • Understanding of basic measurement uncertainty principles
  • Familiarity with trigonometric functions, specifically arctan and sine
  • Knowledge of uncertainty propagation rules for addition, subtraction, multiplication, and division
  • Experience with experimental data analysis in physics
NEXT STEPS
  • Study the principles of uncertainty propagation in measurements
  • Learn about trigonometric functions and their impact on uncertainty
  • Explore methods for calculating maximum and minimum values in experimental data
  • Investigate the application of uncertainty in real-world physics experiments
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Students conducting physics experiments, educators teaching measurement uncertainty, and researchers analyzing experimental data in scientific studies.

cosmicaa
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Homework Statement



I conducted an experiment to find the refractive index of several concentrations of sugar solutions. I now need to find out the final uncertainty of my measurements but am unsure of how to go about calculating it.

Homework Equations



  • I took 2 measurements of length which i estimate the uncertainty to be +/- 0.025cm (let these measurements of length be a & b)
  • I divided these two lengths and took the arctan of them: c=arctan(a/b)
  • I then placed it in this equation: 2sin(c/2+pi/6)

    What happens to the uncertainty?

The Attempt at a Solution



I am not too sure with the trigonometric operators but I assume they don't do anything to the uncertainties. I am guessing that if this is true, then i just use the usual uncertainty rules of +, -, /, * ?

Thanks so much!
 
Physics news on Phys.org
If you don't know, or forget, the rules governing this, there is a simple way of finding out the maximum uncertainty in your calculated answer based on single measurements.
Find the highest possible value of c using (a + uncertainty) divided by (b - uncertainty) then the lowest value by reversing the + and -
Then put those two values into your sin expression to find the highest and lowest possible values of that.
 

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