Calc Angle of Refraction in Opaque Drinking Glass Problem

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To solve the problem of calculating the angle of refraction for an observer looking into a cylindrical opaque drinking glass, Snell's law can be applied, but determining the initial angle is crucial. The observer's position relative to the glass rim and the bottom edge provides necessary geometric relationships. When the glass is empty, the observer sees the bottom edge, while a full glass allows visibility of the center, indicating a change in viewing angles due to refraction. The index of refraction of the liquid, 1.29, is essential for applying Snell's law effectively. Clarifying the angles involved is the key to starting the calculation process.
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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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I would like to know if anyone has found a way to solve this.

Please help.

-U
 
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