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An cylindrical opaque drinking glass has a diameter 3.1 cm and height h, as shown in the figure. An observer's eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled (with a transparent liquid with an index of refraction of 1.18) to the brim, the observer can just barely see the center of the bottom of the glass.

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Calculate the angle θr. Answer in units of degrees.

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