I'm trying to find the uncertainty in [tex]\theta[/tex] where [tex]\theta[/tex] is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\theta=sin^{-1}\frac{n\lambda}{d}[/tex]

in this case, I am assuming there is no uncertainty in [tex]\lambda[/tex].

This is what I tried:

[tex]\delta \theta=\sqrt{(\frac{d\theta}{dd})^2(\delta d)^2}[/tex]

(the total derivative in there should be a partial derivative, but I don't know how to get that symbol)

[tex]\delta \theta=\sqrt{(\frac{\frac{\lambda}{d}}{\sqrt{d^2-\lambda^2}})^2\delta d^2}[/tex]

I think that is right, but if I use the values [tex]\lambda=632.8 nm, d=1.08 \mu m[/tex] and [tex]\delta d =.001 \mu m[/tex] I get an uncertainty of almost 450 degrees. Where am I making my mistake?

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# Homework Help: Error analysis

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