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Problem of the Week 838

The Pains of Imperfect Glass

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Suppose a type of glass is such that:

How much of an original light source will be transmitted through 3 panes of glass?
             |   |   |
             |   |   |
             |   |   |
             |   |   |
Light        |   |   |           You
Source       |   |   |
             |   |   |
             |   |   |
             |   |   |
             |   |   |
             |   |   |
             |   |   |

It is assumed that the panes are parallel and at a small distance from each other, as illustrated. Ignore any loss of light above or below the panes (which is the same as assuming the panes extend infinitely in all four directions).

Source: This problem is due to Johan H. Meyer (University of the Orange Free State, Bloemfontein, South Africa), who posed the more general problem with n panes of glass.

© Copyright 1997 Stan Wagon. Reproduced with permission.

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2 October 1998