I see a large house and many pets in your future

Classical Mechanics Level 5

Fortune tellers use crystal balls to see the future. A fortune teller has a crystal ball with an index of refraction of 1.5 and diameter of 0.2 m. You sit on one side of the ball and the fortune teller sits on the other. She holds up a small red jewel on her side in the equatorial plane of the ball. Let P be the point on the ball nearest to the jewel. How far away in m from P is the image of the jewel on your side?

Hint: the question mark in the image below is an unknown you'll need to figure out as an intermediate step. However, the requested answer is the distance from P, i.e. ? + 0.2 m.

Details and assumptions

  • The jewel is at a distance of 0.8 m from P.

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