Discussion
If a coin at the bottom of a lake appears to be at a depth of 6 m, then the gauge pressure on the coin in pascal is (μ of water is 4/3)
Answer: B
The gauge pressure is \(78.4 \times 10^{3}\) Pa.
The apparent depth is the real depth divided by the refractive index, so the real depth is \(6 \times \frac{4}{3} = 8\) m.
\[ \begin{aligned} p &= h\rho g = 8 \times 1000 \times 9.8 \\ &= 78.4 \times 10^{3}\ \text{Pa} \end{aligned} \]
Using the apparent depth 6 m gives \(58.8 \times 10^{3}\) Pa, and dividing by \(\frac{4}{3}\) instead of multiplying gives \(4.5\) m and about \(44 \times 10^{3}\) Pa.
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