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A tall cup of diameter D is partially filled with a liquid with the refraction index n to a height of Hwater. A student looks downward just over the left rim of the cup at an angle pheta with the water's surface. At this angle, the refraction of light at the water's surface just barely allows her to see the bottom-right corner of the cup. A sketch of the path of light is shown in the image. Derive the formula for the height of the cup Hcup. Calculate its numerical value for n = 1.33 (water), D = 14.64 cm, Hwater = 7.8 cm, and angle pheta = 40.47 degrees.

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