Ships in the Night

You are keeping watch on the deck of a ship at night. You are trying to keep a steady distance from your sister ship, which is sailing alongside you, but it is difficult as you can't see them properly in the night.

Luckily you have an accurate light meter, and both ships have identical lamps on their bows. The bow of your ship is \(\SI{50} {\m}\) away and the intensity of light from its lamp where you stand is \(\SI{80}{\W \m^{-2}}\). The intensity of light from the lamp on the other ship is \(\SI {5}{\W \m^{-2}}\).

Assuming the light from both lamps spreads equally in all directions, how far (in \(\text{m}\)) away is the lamp on the other ship?

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