Optics - Apparent Change in Position due to Media

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king vitamin
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Homework Statement


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.


Homework 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] .

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).
 
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Answers and Replies

  • #2
king vitamin
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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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