On error analysis of my practical

[Delzac]

[Urgent]On error analysis of my practical

Homework Statement

well, the aim of the practical is to calculate the speed of light using LED, oscilloscope and varying fiber optics cable.

i have my results as follows :

L /m t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 taverage

5.00 (28 30 28 28 28 28 28 28 30 28) 28.4

10.00 (60 62 60 60 60 60 60 60 60 60) 60.2

15.00 (76 76 78 76 76 76 76 76 76 76) 76.2

20.00 (102 100 102 102 102 102 102 102 100 102) 101.6

The equation used is $$c = n \frac{\lambda}{t}$$

We are to plot a graph of L versus time.

The problem now is calculating the error of y.

Do we use

Least Square Method( where $$\sigma_i = \sigma$$) OR
Least Square Method( Where each y, has its own $$\sigma_i$$)

We know that L is the y-axis in this case, however no multiple values of L has been taken. So every y, has the same $$\sigma$$. However, time has been taken mutiple times, do we use LSM(Where each y, has its own $$\sigma_i$$) on it? But time is the x-axis in this case.

So what should i use or do?

Any help will be appreciated. Thanks

 

[Delzac]

Anyway, since gradient is speed of light, the graph has to be a straight line.

 

[m2003]

I would first like to commend you on your detailed and thorough approach to your practical experiment. It is important to carefully consider and analyze any potential errors in your results in order to ensure the accuracy and reliability of your findings.

In regards to your question about calculating the error of y, it would depend on the specific requirements and guidelines of your experiment. Generally, the least square method is used to calculate the overall error in a set of data, taking into account the errors in both the dependent and independent variables. In this case, since the dependent variable is L and the independent variable is time, you could use the LSM method where each y has its own \sigma_i. This would take into account any potential errors in the measurement of time, which could affect the accuracy of your results.

However, if your experiment does not require such a detailed analysis of errors, you could also use the simpler approach of using the overall \sigma for all y values, as you have suggested. This would still provide a general estimate of the error in your results.

Ultimately, the best approach would be to consult with your instructor or refer to any guidelines provided for your experiment to determine the most appropriate method for calculating the error in your results. It is always important to follow the recommended procedures in order to ensure the validity of your findings. Good luck with your analysis!