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Homework Help: Angular separation between two wavelengths

  1. May 21, 2010 #1
    1. using differentiation,find the angular separation in arc minutes in second order for two wavelengths 589.0 and 589.6 nanometers



    2. d sin([tex]\theta[/tex])=m ([tex]\lambda[/tex])



    3. i try to use D=[tex]\delta[/tex][tex]\theta[/tex]/[tex]\delta[/tex][tex]\lambda[/tex]
    by differentating d sin([tex]\theta[/tex])=m ([tex]\lambda[/tex]) i got d/m sec(thetha).this equation can be further change to D=(sinA+sinB)/[tex]\lambda[/tex]sinB.
    i assumed D is the separation between the wavelengths.is it the correct way to approach the problem??
     
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  3. May 21, 2010 #2

    vela

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    No, the problem is asking for the angular separation Δθ.
     
  4. May 21, 2010 #3
    thanks.now i know how to solve it. is it Δlambda/Δθ= d/m cosθ? and by using small angle approximation,cos theta = 1.so Δθ= Δlambda*m/d? i forgot to put extra info:d=(1/600)mm
     
  5. May 21, 2010 #4

    vela

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    I think you need to be a little more careful because the problem asks you to find the separation to second order, not just first order.
     
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