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Optics - Apparent Change in Position due to Media

  1. Apr 14, 2009 #1

    king vitamin

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    Gold Member

    1. The problem statement, all variables and given/known data
    A plane slab of glass of thickness t and index n is inserted between an observer's eye and a point source. Show that the point source appears to be displaced to a point closer to the observer by approximately [(n-1)/n]t. Use small-angle approximations.


    2. Relevant equations

    Snell's Law and trig relations/approximations. I don't have a way to scan in the diagrams I've drawn, but a good one I've found is here: http://homepage.mac.com/cbakken/obookshelf/image033.gif [Broken] .

    3. The attempt at a solution

    Previously I've solved for the apparent change in position of an object placed in a media of higher index of refraction which is analogous to the answer. The problem here is that both the observer and the object are outside of the media, so I can't seem grasp on to any equations relating distance of object, apparent distance of object, and slab thickness. I've been using approximations such as tan[theta]=sin[theta] so I can use Snell's Law, but since the object is located outside of the media I'm not sure how to use the refraction angle for equations. Any hints would be appreciated (I feel like there's just an approximation I'm not thinking of).
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 14, 2009 #2

    king vitamin

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    Gold Member

    Nevermind, I've solved the problem (the trick was to consider another point further back from the object, where a person from inside the glass slab would see the object located).
     
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