Problem 3 Coin Magic We have placed a coin at the center of a glass that has radius
R
and some unknown height. When we look into the glass, we see the edge of the bottom of the glas as shown. Suppose we fill the glass to the top with a liquid that has index of refraction
n
and we now see the coin. Assuming we have not changed our positioning, show that the lieight of the glass must be:
h=2R\sqrt((n^(2)-1)/(4-n^(2)))

Question

Problem 3 Coin Magic We have placed a coin at the center of a glass that has radius

R

and some unknown height. When we look into the glass, we see the edge of the bottom of the glas as shown. Suppose we fill the glass to the top with a liquid that has index of refraction

n

and we now see the coin. Assuming we have not changed our positioning, show that the lieight of the glass must be:

h=2R\sqrt((n^(2)-1)/(4-n^(2)))

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