Imagine that while in Rome you are admiring the famous Fontana dei Quattro Fiumi
ID: 1443860 • Letter: I
Question
Imagine that while in Rome you are admiring the famous Fontana dei Quattro Fiumi, or the Fountain of the Four Rivers, in the center of Piazza Navona. You think about retrieving a coin at the bottom of the fountain. Light from the coin reaches your eye at an angle of 37 below the horizontal (the angle between your line of sight and the vertical normal line to the water is 53 ). The depth of the fountain is 0.40 m and your height is 1.7 m (1.3 m above the water level).
Where is the coin? Determine the horizontal distance to the coin from where you are standing.
Explanation / Answer
n1 sin(B1) = n2 sin(B2)
==> 1.00 sin(53) = 1.33 sin(B2)
==> B2 = 36.904 degrees
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x2 = y2 tan(B2) = 0.40 tan(36.904) = 0.30037 m
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x1 = y1 tan(B1) = 1.3 tan(53) = 1.72516 m
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d = x1 + x2 = 1.72516 + 0.30037 = 2.03 m