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 1.90 $\mathrm{cm} )$ 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 1.75 $\mathrm{cm} )$ is placed directly over it, the bubble can be seen by looking down into the cube. What is the range of the possible depths of the air bubble beneath the surface?