Hypnotoad
- 35
- 0
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?
\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?