Index of Refraction Uncertainty Problem

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SUMMARY

The discussion focuses on calculating the uncertainty in the index of refraction using the formula n=sin⁡((A+D_m)/2)/sin⁡(1/2 A), where A is the angle of refraction and Dm is the angle of minimum deviation. The user reports that applying propagation of error equations results in an uncertainty expressed in degrees, which is confirmed as correct since indices of refraction are dimensionless. An example trial provided includes A = 59.97 degrees and Dm = 45.6 degrees, illustrating the calculations involved.

PREREQUISITES
  • Understanding of Snell's Law and refraction principles
  • Familiarity with the concept of minimum deviation in optics
  • Knowledge of error propagation techniques in measurements
  • Basic trigonometry and sine function applications
NEXT STEPS
  • Study the derivation of the index of refraction formula in optics
  • Learn advanced error propagation methods for complex measurements
  • Explore the impact of wavelength on the index of refraction
  • Investigate the relationship between angle of refraction and critical angles
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Students in physics or engineering, optical scientists, and anyone involved in experimental measurements of light refraction and uncertainty analysis.

Browntown
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Homework Statement
Trying to find the uncertainty in individual measurements of the index of refraction of a prism
Relevant Equations
n=sin⁡((A+D_m)/2)/sin⁡(1/2 A)
index equation.png

A is the angle of refraction (~60 degrees) and Dm is the angle of minimum deviation that was different for each of the spectral lines associated to one of the six wavelengths measured.
The problem I'm having is when I use equations of propagation of error to find the uncertainty in these indices, the uncertainty ends up coming with units of degrees which I'm almost certain is correct as indices have no units.

An example trial is: A = 59.97 degrees and Dm = 45.6 degrees

Thank you.
 
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Browntown said:
Homework Statement: Trying to find the uncertainty in individual measurements of the index of refraction of a prism
Homework Equations: n=sin⁡((A+D_m)/2)/sin⁡(1/2 A)

View attachment 250256
A is the angle of refraction (~60 degrees) and Dm is the angle of minimum deviation that was different for each of the spectral lines associated to one of the six wavelengths measured.
The problem I'm having is when I use equations of propagation of error to find the uncertainty in these indices, the uncertainty ends up coming with units of degrees which I'm almost certain is correct as indices have no units.

An example trial is: A = 59.97 degrees and Dm = 45.6 degrees

Thank you.
Please post your working. (Not as an image.)
 

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