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Snell's law demonstration?

  1. Dec 29, 2015 #1
    I can't figure out why my demonstration of snell's law fails, that's the demonstration: (I used a photo)
    I think it fails because the function t (HO) represents a line and so the concept of minimum is not defined, when I take the derivative and equal it to 0 I'm considering the case when the line is parallel to the x axis (the first derivative gives me the angular coefficient and when I equal it to 0 the line is parallel) (considering as y the time and as x HO)

    Is that the problem? ( I know the real demonstration but i want to understand why this variant doesn't work)
     

    Attached Files:

  2. jcsd
  3. Dec 30, 2015 #2
    ##AO\sin\theta_1=AH##
     
  4. Dec 30, 2015 #3
    But... θ1 is the angle whit the vertical
     
  5. Dec 30, 2015 #4
    You are right. May be better a simpler geometry.
    Let ##A(x_1,y_1)## and ##B(x_2,y_2)## the end points and ##O(x,0)## the point than we need. Write the total time and take derivation ##d/dx(t)=0##.
     
    Last edited: Dec 30, 2015
  6. Jan 8, 2016 #5
    yep it is preferable to use simple geometry to demonstrate
     
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