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A large Lucite cube (n = 1.59) has a small air bubble (a defect in the casting process) below one surface. When a penny (diameter 1.9 cm) is placed directly over the bubble on the outside of the cube, the bubble cannot be seen by looking down into the cube at any angle. However, when a dime (diameter 1.634 cm) is placed directly over it, the bubble can be seen by looking down into the cube.

What are the upper and lower bounds of the range of the possible depths of the air bubble beneath the surface?

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