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Question

A person looking into an empty container is able to see the far edge of the container's bottom as shown in this Figure. The height of the container is $$ h, $$ and its width is $$ d $$. When the container is completely filled with a fluid of index of refraction $$ n $$ and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom as shown in this Figure. For what range of values of $$ n $$ will the center of the coin not be visible for any values of $$ h $$ and $$ d $$?

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Solution

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For $$ n=1, h=0 . $$ For $$ n=2, h=\infty . $$ For $$ n>2, h $$ has no real solution.

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