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Homework Help: Help with critical angle calculation

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A penny sits at the bottom of a pool of water (n=1.33) at a depth of 3.0m. If the observer 1.8m tall stands 30cm away from the ledge, how close to the side can the penny be and still be visible to the observer. Suppose there is another penny 10 times farther away than the 1st one, will a light ray going from this new penny to the top edge of the pool emerge from the water ? And if yes, what is the angle made by the light ray?

    2. Relevant equations
    To still be visible, the angle should be less than critical angle, is that correct? but I can't figure this out .. please help

    3. The attempt at a solution
    real depth = 3.0 so apparent depth can be calculated to be 3/1.33 = 2.25 m.
    I can also calculate the critical angle with Snell's sin(theta) = 1.33 (since sin 90 = 1). So theta = 48.75 . Which means that the angle has to be less that 48.75 for the penny to be visible.
    Now how do I get the distance from this?

    Please help I have a test on Wednesday. Thanks
    Last edited: Feb 2, 2009
  2. jcsd
  3. Feb 3, 2009 #2
    Why not turn the problem around? Imagine a light ray coming from the observer's eye, grazing the edge of the pool, and going down into the water. Where would it reach the bottom?

    Now you've got that distance sorted out you'll be able to attack the next part of the problem.
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