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I need help with calculating the uncertainty of the refractive index of air which has been obtained by the equation in this document: $$n_{\text{air,atm}}=(\frac{N}{P/P_{\text{atm}}})(\frac{\lambda}{2L})+n_{\text{vacuum}}$$

My experiment was quite similar to this, and my results were also similar. I just really don't understand how they came to their uncertainty. All my uncertainty values are over 1 which I know isn't correct. I was hoping someone could maybe write the equation used or atleast get me started in how to form an equation to figure out the uncertainty. I'm really struggling and any help will be appreciated.

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  • $\begingroup$ I've added the homework-and-exercises tag. In the future, please add this tag to this type of problem. $\endgroup$ – Ben Crowell Nov 19 at 3:27
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The usual methods for propagating uncertainties through functions should apply. For example, if $$ A=BC $$ where $B$ and $C$ are measured quantities with uncertainties $\Delta B$ and $\Delta C$ respectively, then $$ \left(\frac{\Delta A}{A}\right)^2 = \left(\frac{\Delta B}{B}\right)^2 + \left(\frac{\Delta C}{C}\right)^2 $$ would allow you to find the uncertainty for $A$.

See e.g. Wikipedia for a summary.

Does this help?

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  • $\begingroup$ I know that but my uncertainty is over 1 which is incorrect. They also mention in the link that they have an uncertainty of ± 1 for the fringes. I just don't understand how they got such a low uncertainty for the refractive index with an uncertainty like that. Also I know my uncertainty is incorrect as it shouldn't be over 1. Could you help any further ? Thanks $\endgroup$ – Cinna Nov 19 at 4:34
  • $\begingroup$ @Cinna I had a closer look at the text you linked. Their final estimate does seem remarkably precise, so I'd guess that they miscalculated at some point. As for your uncertainties, I can't say for sure without more information, but why should uncertainties not be greater than 1? $\endgroup$ – hiccups Nov 19 at 6:12

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