Solution to 1996 Problem 56


We use Snell's equation

\begin{align*}1.33 \sin \theta_1 = \sin \theta_2\end{align*}
where \theta_1 is the angle the the light makes with the normal below the surface of the water and \theta_2 is the angle that the light makes with the normal above the water. The maximum value of \sin \theta_2 is 1, so total internal reflection occurs when

\begin{align*}\theta_1 = \sin^{-1} \left(1/1.33\right) = \boxed{48.75^{\circ}}\end{align*}
Therefore, answer (C) is correct.


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