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Geometric Optics Gradients

  1. Jun 23, 2007 #1
    I'm sure many of you guys have seen the videos of a beam of light (namely a laser of some sort) pass through a volume of liquid in which there is a gradient of index of refraction from the bottom of the tank to the top. Think of a sugar solution in which more sugar collects at the bottom and gradually tappers off at toward the top.

    The beam of light upwardly strikes the side of the tank at an arbitrary angle. This light then bends until it gets parallal to the bottom of the tank. This is were geometric optics says it would then keep moving straight through the tank without changing it's direction any more because there is no longer a change in index of refraction along the direction of motion.

    However, that is not the case. The light actually keeps bending through the parallal postion and then bends downward from there.

    Here are the various reasons I have come up with as to why it happens:

    1. The gradient is not perfect in the real world, therefore the light will end up bending downwards. Think of a ball at the top of a cone, any movement will set it into kinetic motion. This is kind of a knee jerk response, that I can't live with.

    2. The light beam actually starts reflecting off of the gradient as the angle gets larger (critical angle). This explains why the beam seems to get wider and dimmer at the top of its curve also. This doesn't seem to provide a good explaination because light typically reflects off of hard transitions. Can it reflect off of gradients?

    3. Traditional geometric optics can not explain this phenomenon. We must look to Huygen's Principle to further explain this observation.

    What do you guys think, how would you explain it? BTW I noticed that basic laws of geometric optics would not reproduce what really happened after writing a spreadsheet to simulate the "fish tank" experiment.
     
  2. jcsd
  3. Jun 24, 2007 #2

    Doc Al

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    Staff: Mentor

    Good observation! You can't use simple geometric "ray" optics to explain this, you need wave optics (Huygen's will work). A horizontal beam gets refracted downward since it's not infinitely narrow, but has a finite cross-section: since there's a vertical gradient, different parts of the beam have different speeds, curving the entire beam downward.

    As I'm sure you are aware, this same effect explains mirages. (With the gradient reversed, of course.)
     
  4. Jun 24, 2007 #3
    Huh? You can't just use Fermat's principle on the ray? How do you think this is different to interface refraction?
     
  5. Jun 24, 2007 #4

    Doc Al

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    Point taken! Perhaps I'm being sloppy about the meaning of "geometric optics", but I was responding to the question of how a "ray" can bend when there's no change in refraction index along its direction of motion. Fermat's principle still applies, of course.
     
  6. Jun 24, 2007 #5
    I was leaning toward number three, but I did not know if light would reflect off of a true gradient. Are there any cases in which it does reflect off of a pure gradient?
     
  7. Jun 24, 2007 #6

    Claude Bile

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    Science Advisor

    Yes, light can be reflected off refractive index gradients, most optic fibres are graded-index rather than step-index fibres as the graded-index profile assists in managing signal dispersion.

    Claude.
     
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