Index of Refraction Uncertainty Problem

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The discussion revolves around calculating the uncertainty in the index of refraction for a prism using angles of refraction and minimum deviation. The angle of refraction (A) is approximately 60 degrees, and the angle of minimum deviation (Dm) varies for different spectral lines. The user encounters an issue where the propagation of error calculations yield uncertainties in degrees, which seems incorrect since indices of refraction are unitless. An example trial is provided with specific angle measurements, highlighting the need for clarification on the correct approach to determine uncertainty. The conversation emphasizes the importance of ensuring that the final uncertainty aligns with the unitless nature of the index of refraction.
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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