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Homework Help: Light Ray Path

  1. May 17, 2008 #1

    Air

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    1. The problem statement, all variables and given/known data
    The diagrams below illustrate the formation of a rainbow. Figure 1 shows the general arrangement and Figure 2 shows the path of a ray through a raindrop with the centre of the raindrop is labelled O.

    Figure 1:
    Raindrop1.jpg

    Figure 2:
    Raindrop2.jpg

    a.)
    Where the ray enters the raindrop in Figure 2, mark the angle of incidence i and the angle of refraction, r.

    b.)
    Figure 2 is drawn to scale. By taking suitable measurements, show that the refractive index of water is about 1.3.


    2. Relevant equations
    [itex]\mu = \frac{\sin i}{\sin r}[/itex]


    3. The attempt at a solution
    a.)
    Raindrop2Attempt.jpg
    ^ Have I labelled it correct?

    b.)
    I measured the angle that I have labelled above and got [itex]i = 25^\circ[/itex] and [itex]r = 35^\circ[/itex] and this gives [itex]\mu = 0.74[/itex]. This is incorrect. The correct answer is [itex]i = 53, \ r = 39, \ \implies \mu = 1.27[/itex]. Where have I gone wrong here?
     
  2. jcsd
  3. May 17, 2008 #2

    Redbelly98

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    The normal should be perpendicular to the water's surface.
     
  4. May 17, 2008 #3

    Air

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    So, is it like this?

    Raindrop2Attempt2.jpg
     
  5. May 17, 2008 #4

    Air

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    Or, is it like this? :confused:

    Raindrop2Attempt3.jpg
     
  6. May 17, 2008 #5
    You just seem to be drawing random lines lol...

    The normal line on a spherical surface at some point P is always the line that goes from P through the center of the circle.

    In other words; if you draw a straight line through the center of a circle, then at the points where it intersects the circle the angle between the line and the circle (at that point) is exactly 90 degrees, or perpendicular.
     
  7. May 17, 2008 #6

    Air

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    Oooh, I understand now. I guess it is this:

    Raindrop2Attempt4.jpg

    Am I correct?
     
    Last edited: May 17, 2008
  8. May 17, 2008 #7

    Redbelly98

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    Yes, that looks good.
     
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