zdenton
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Homework Statement
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:
d=\frac{1}{300000}
l=0.20
\Delta l=0.001
y=0.043
\Delta y=0.005
Homework Equations
\sin\alpha=\frac{\lambda}{d}
\tan\alpha=\frac{y}{l}
The Attempt at a Solution
I combined these equations to end up with:
\lambda=d\times\sin\left(\arctan\left(\frac{y}{l}\right)\right)
The problem is that I don't know how to estimate an uncertainty for this equation. I know that for simple equations like y=q\times r the uncertainty is \Delta y=\left(\frac{\Delta q}{q}+\frac{\Delta r}{r}\right)\times y. 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 \lambda=d\times\sin\left(\arctan\left(\frac{y}{l}\right)\right), it would be greatly appreciated.