The following discussion of Snell's Law of Refraction* (named after Willebrord Snell, 1580-1626) is needed for Light, sound, and other waves travel at different speeds, depending on the media (air, water, wood, and so on) through which they pass. Suppose that light travels from a point $A$ in one medium, where its speed is $v_1$, to a point $B$ in another medium, where its speed is $v_2$. Refer to the figure, where the angle $\theta_1$ is called the angle of incidence and the angle $\theta_2$ is the angle of refraction. Snell's Law, which can be proved using calculus, states that
$$
\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}
$$
The ratio $\frac{v_1}{v_2}$ is called the index of refraction. Some values are given in the table shown to the right.
(FIGURE CAN'T COPY)
The index of refraction of light in passing from a vacuum into water is 1.33 . If the angle of incidence is $40^{\circ}$, determine the angle of refraction.
$$
\begin{array}{|lc|}
\hline {\text { Some Indexes of Refraction }} \\
\hline \text { Medium } & \text { Index of Refraction }{ }^{\dagger} \\
\hline \text { Water } & 1.33 \\
\text { Ethyl alcohol }\left(20^{\circ} \mathrm{C}\right) & 1.36 \\
\text { Carbon disulfide } & 1.63 \\
\text { Air }\left(1 \text { atm and } 0^{\circ} \mathrm{C}\right) & 1.00029 \\
\text { Diamond } & 2.42 \\
\text { Fused quartz } & 1.46 \\
\text { Glass, crown } & 1.52 \\
\text { Glass, dense flint } & 1.66 \\
\text { Sodium chloride } & 1.54 \\
\hline
\end{array}
$$