How to Calculate the Observer's Viewing Angle in a Refraction Problem?

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To calculate the observer's viewing angle in the refraction problem involving a cylindrical drinking glass, the observer's position relative to the glass's rim and bottom is crucial. The observer can see the bottom edge when the glass is empty and the center when filled, indicating a change in viewing angle due to refraction. Snell's law can be applied, but determining one of the angles is essential for the calculation. The index of refraction of the liquid, given as 1.29, plays a significant role in this calculation. The discussion concludes with the original poster finding a solution to the problem.
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A cylindrical opaque drinking glass has a diameter of 4.7 cm and a hieght h. An observer's eye is placed to where they are just barely looking over the rim of the glass. When the glass is empty, the observer can just barely see the edge of the bottom of the glass. When the glass is filled to be brim, the observer can just barely see the center of the bottom of the glass. The liquid in teh glass has an index of refraction of 1.29. Calculate the angle at which the observer is looking into the glass.

I could use Snell's law if I could figure out one of the angles in the equation. I am not sure on how to start this problem. Does anyone have an idea on how to obtain one of the angles from the information given. I know it has to be something simple that I am not thinking of.
 
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never mind
found a way

thanks anyways guys!

-U
 

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