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Critical angle optics problem

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    A point source of light is located 3.56 m below the surface of a large lake of clear, but contaminated, water (Lake Ontario, where n = 1.28). Find the area of the largest circle on the lake's surface through which light coming from the source can emerge into the air.


    2. Relevant equations



    3. The attempt at a solution
    Not sure where to start
     
  2. jcsd
  3. Nov 24, 2007 #2

    mgb_phys

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    Lookup 'critical angle'
     
  4. Nov 24, 2007 #3
    ok:
    [tex] sin(\theta)_c=\frac{n_air}{n_water}[/tex]
    [tex] \theta_c= 51.37[/tex]
    I use some trig to find the radius which is:
    [tex] r=hcos(\theta_c)[/tex]
    And I can find the area from there, correct?
     
  5. Nov 24, 2007 #4

    mgb_phys

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    Yes - but draw a sketch just to make sure you have the angle the right way round - it's always tricky when it's near 45deg.
     
  6. Nov 24, 2007 #5
    oops.
    that [tex] r=hcos(\theta_c)[/tex] should be a [tex] r=htan(\theta_c)[/tex]
     
  7. Nov 24, 2007 #6
    I get 90.48 m^2 but it is incorrect
     
  8. Nov 24, 2007 #7

    mgb_phys

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    Theta is the angle between the ray that would just exit and the normal to the surface.
    So by similair triangles it is also the internal angle between the ray and a line straight up from the surface to the source.

    So the radius of the patch on the surface is tan(theta) * depth. The area is then of course pi r^2.

    (I get 65.5m^2)
     
  9. Nov 24, 2007 #8
    Funny calc mistake,
    but i got 62.36 m^2 and that is he correct answer
     
  10. Nov 24, 2007 #9

    mgb_phys

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    oops - typed it out wrong! Always check your arithmatic!
     
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