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Rank the material according to their indices of refraction

  1. Sep 28, 2013 #1
    1. The problem statement, all variables and given/known data

    In the figure below (see image in color), light travels from material 'a', through three layers of other materials with surfaces parallel to one another, and then back in to another layer of material 'a'. The refractions (but not the associated reflections) at the surfaces are shown. Rank the materials according to their indices of refraction, greatest first.


    2. Relevant equations

    Laws of Refraction:

    1. If the ray is bent so that it sits between the normal and incident beam, N2>N1
    2. If the ray is bent so that it sits outside the normal and incident beam, N1>N2

    3. The attempt at a solution

    See image in black & white. Using the relevant equations, I was able to set the following boundaries:

    Nb>Na
    Nc<Nb
    Nd>Nc
    Na<Nd

    The problem is that I still don't have enough information to order the indices of refraction. For example, the following could be true:

    Nd > Nb > Nc > Na

    But I really don't have any evidence that supports Na > Nc or that Nd > Nb.

    The correct answer is: Nd > Nb > Na > Nc

    Am I supposed to estimate the angles and draw the rest of the boundaries from that?

    Thanks in advance, MrMoose
     

    Attached Files:

  2. jcsd
  3. Sep 28, 2013 #2

    Doc Al

    User Avatar

    Staff: Mentor

    To compare any two regions, all you need do is compare the angles of those rays. Eyeball it.
     
  4. Sep 28, 2013 #3
    Thanks Doc Al, I figured it was just an eyeball thing, so let me see if I see it... so to speak.

    Given my original original boundary conditions, my only questions were on the relationship between Na and Nc, and Nd and Nb.

    Right off the bat, I can see that θd < θb

    Given the general equation: n2 * sin(θ2) = n1 * sin(θ1), I know the following:

    If θ2<θ1, it follows that N2<N1, therefore

    Nd >Nb

    Making the judgement call on θa and θc is not quite so obvious though. I had to pull out my protractor. In the end, I did find that θa < θc. Therefore, it follows that:

    Na > Nc

    And the final answer is:

    Nd > Nb > Na >Nc
     
  5. Sep 28, 2013 #4

    Doc Al

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    Staff: Mentor

    Looks good to me! :thumbs:
     
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