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In atomic spectra experiment I came across with error propogation in the nonlinear equation:

[itex]\lambda=d\times\sin(\theta)[/itex] which gives the wavelength when first order constructive interference is observed at a given angle with respect to the normal of the plane of the grating. The relative error I am interested in is [itex]\frac{\Delta \lambda}{\lambda}[/itex]. In the laboratory manual it is stated without proof to be:

[itex]\frac{\Delta \lambda}{\lambda}=\sqrt{(\frac{\Delta \theta}{\theta})^2+(\frac{\Delta d}\{d})^2}[/itex] I am pretty confused about it since I could not manage to verify it. I need a demonstration on why the relative error in wavelength is given by the preceding expression. I would be glad if anyone can guide me with references or suggestions.

Thanks in advance

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# Relative Error Propogation in Equations

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