Index of Refraction Uncertainty Problem

In summary, the conversation involved finding the uncertainty in individual measurements of the index of refraction of a prism using equations of propagation of error. The uncertainty was found to have units of degrees, which is correct since indices have no units. An example trial with A = 59.97 degrees and Dm = 45.6 degrees was given. The formula used was n = sin((A+Dm)/2)/sin(1/2A).
  • #1
Browntown
18
0
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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  • #2
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.)
 

FAQ: Index of Refraction Uncertainty Problem

1. What is the index of refraction uncertainty problem?

The index of refraction uncertainty problem refers to the challenge of accurately measuring the refractive index of a material due to factors such as experimental error, variations in the material's composition, and the effects of temperature and pressure.

2. How is the index of refraction uncertainty calculated?

The index of refraction uncertainty is typically calculated using the formula: Δn = n2 - n1, where n1 is the minimum measured refractive index and n2 is the maximum measured refractive index. This provides a range of possible values for the refractive index with a certain level of confidence.

3. What are some common sources of uncertainty in measuring the index of refraction?

Common sources of uncertainty in measuring the index of refraction include limitations in the precision of measurement equipment, variations in the material sample being tested, and external factors such as temperature and pressure.

4. How can the index of refraction uncertainty be minimized?

The index of refraction uncertainty can be minimized by using more precise and accurate measurement equipment, taking multiple measurements and averaging the results, and controlling for external factors that may affect the refractive index.

5. Why is it important to account for the index of refraction uncertainty in scientific experiments?

Accounting for the index of refraction uncertainty is important because it allows for a more accurate and reliable interpretation of experimental results. Without considering this uncertainty, the true value of the refractive index may be misrepresented, leading to incorrect conclusions or inaccurate predictions.

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