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Error analysis

  1. Dec 14, 2004 #1
    I'm trying to find the uncertainty in [tex]\theta[/tex] where [tex]\theta[/tex] is given by:

    [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?
     
  2. jcsd
  3. Dec 14, 2004 #2

    dextercioby

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    1.Click on this:[tex] \partial [/tex].
    2.U assumed "n=1",else that derivative should have included the product [itex] n\lambda [/itex].
    3.If [itex] n\neq 1 [/itex],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.
     
  4. Dec 14, 2004 #3
    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.
     
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