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Refraction Problem

  1. Oct 24, 2008 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    2. Relevant equations


    3. The attempt at a solution
    Basically, I tried to use triangles to find the angles. But I don't know how as it seems I'm only given one side of the triangles.
     
  2. jcsd
  3. Oct 24, 2008 #2

    LowlyPion

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    I think they want you to consider the effect of Snell's Law here.

    [tex] \frac{n_1}{n_2} = \frac {Sin \theta_1}{Sin \theta_2} [/tex]
     
  4. Oct 24, 2008 #3
    You mean
    [tex] \frac{n_1}{n_2} = \frac {Sin \theta_2}{Sin \theta_1} [/tex]

    So lets say n1 = n2 when the glass is empty because the angle of incident is equal to the angle of refraction. When the glass is full, n2 = 1.22 and everything else is unknown. So how would I go about finding just theta r, which is theta_1 in this case?
     
  5. Oct 24, 2008 #4

    LowlyPion

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    Yes. Sorry for the hurried typo.

    With respect to the problem you know the angle of sight over the top is h/(h2 + d2)1/2

    And the angle it makes in the liquid is h/(h2 + d2/4)1/2

    And you know they are related by the 1.22 then don't you?

    You know D so solve for h. Having h in hand then you can figure the angle directly.
     
    Last edited: Oct 24, 2008
  6. Oct 25, 2008 #5
    Thanks a lot lowlypion.

    I had a little trouble figuring out why your values didn't work, but in the end I found that the values were actually:

    d/(d2 + h2)1/2 for the top angle

    and

    (d/2)/(d2/4 + h2)1/2 for the liquid angle.

    All in all though, you greatly helped me. Thank you so much!
     
  7. Oct 25, 2008 #6

    LowlyPion

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    My apologies. I relied on the Hyperphysics link that shows the angle with the surface rather than with the normal.

    http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html#c3

    [​IMG]
     
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