error analysis

[Hypnotoad]

I'm trying to find the uncertainty in \theta where \theta is given by:

\theta=sin^{-1}\frac{n\lambda}{d}

in this case, I am assuming there is no uncertainty in \lambda.

This is what I tried:

\delta \theta=\sqrt{(\frac{d\theta}{dd})^2(\delta d)^2}

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

\delta \theta=\sqrt{(\frac{\frac{\lambda}{d}}{\sqrt{d^2-\lambda^2}})^2\delta d^2}

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

[dextercioby]

1.Click on this: \partial .
2.U assumed "n=1",else that derivative should have included the product n\lambda .
3.If n\neq 1 ,then you should include "n" in the derivative (under the square root) and redo your calculations.
4.If "n=1",then it's either the numbers are badly chosed,or u ****ed those calculations.

Daniel.

[Hypnotoad]

1. Thanks for the latex lesson
2. n=1
3. Turns out it was just my math. Although I did that calculation at least 4 or 5 times and kept getting the same answer before. I don't know what I was doing wrong, but it works much better now.