(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have conducted an experiment which attempts to calculate the range of the visible light spectrum. Basically white light was shined through a diffraction grating (300 lines/mm) and diffraction theory is applied to calculate the wavelength.

So, here are the variables:

[tex]d=\frac{1}{300000}[/tex]

[tex]l=0.20[/tex]

[tex]\Delta l=0.001[/tex]

[tex]y=0.043[/tex]

[tex]\Delta y=0.005[/tex]

2. Relevant equations

[tex]\sin\alpha=\frac{\lambda}{d}[/tex]

[tex]\tan\alpha=\frac{y}{l}[/tex]

3. The attempt at a solution

I combined these equations to end up with:

[tex]\lambda=d\times\sin\left(\arctan\left(\frac{y}{l}\right)\right)[/tex]

The problem is that I don't know how to estimate an uncertainty for this equation. I know that for simple equations like [tex]y=q\times r[/tex] the uncertainty is [tex]\Delta y=\left(\frac{\Delta q}{q}+\frac{\Delta r}{r}\right)\times y[/tex]. Unfortunately I don't know how to apply this to a more complex equation. If anyone could lead me in the right direction as to an equation which would give the uncertainty for [tex]\lambda=d\times\sin\left(\arctan\left(\frac{y}{l}\right)\right)[/tex], it would be greatly appreciated.

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# Uncertainty propagation visible light spectrum

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