Calculating the overall uncertainty of my measurements

In summary, the student conducted an experiment to find the refractive index of sugar solutions and now needs to calculate the uncertainty of their measurements. They took two measurements of length with an estimated uncertainty of +/- 0.025cm and used trigonometric operators to find the final uncertainty. They are unsure about the effect of these operators on the uncertainty and are looking for a way to find the maximum uncertainty in their calculated answer.
  • #1
cosmicaa
1
0

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!
 
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  • #2
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.
 

FAQ: Calculating the overall uncertainty of my measurements

1. How do I calculate the overall uncertainty of my measurements?

To calculate the overall uncertainty of your measurements, you need to first determine the uncertainties associated with each measurement. This can be done by taking multiple measurements and calculating the average value and standard deviation. Once you have the uncertainties for each measurement, you can use the root sum of squares method to find the overall uncertainty by adding the individual uncertainties in quadrature.

2. Why is it important to calculate the overall uncertainty of my measurements?

Calculating the overall uncertainty of your measurements is important because it gives you a better understanding of the accuracy and precision of your data. It allows you to quantify the potential errors and variability in your measurements, which is crucial for drawing reliable conclusions and making informed decisions based on your data.

3. Can I just use the largest uncertainty for my overall uncertainty?

No, it is not appropriate to simply use the largest uncertainty for your overall uncertainty. This approach does not take into account the contributions of all the individual uncertainties and can lead to an overestimation of the overall uncertainty. It is important to use the root sum of squares method to properly calculate the overall uncertainty.

4. How can I reduce the overall uncertainty of my measurements?

There are several ways to reduce the overall uncertainty of your measurements. One way is to improve the precision of your measuring instruments. This can be done by using more accurate equipment or taking multiple measurements and averaging them. Another way is to minimize the sources of error, such as environmental factors or human error. Proper calibration and following standard procedures can also help reduce the overall uncertainty.

5. Is there a limit to how small the overall uncertainty can be?

There is no definitive limit to how small the overall uncertainty can be, as it depends on the precision and accuracy of your measurements. However, it is important to note that the overall uncertainty should not be smaller than the smallest uncertainty associated with any individual measurement. If the overall uncertainty is significantly smaller, it may be an indication of an error in your calculations or measurements.

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