The following discussion of Snell's Law of Refraction*...

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) Ptolemy, who lived in the city of Alexandria in Egypt during the second century $\mathrm{AD}$, gave the measured values in the following table for the angle of incidence $\theta_1$ and the angle of refraction $\theta_2$ for a light beam passing from air into water. Do these values agree with Snell's Law? If so, what index of refraction results? (These data are of interest as the oldest recorded physical measurements.) $$ \begin{array}{|llll|} \hline \boldsymbol{\theta}_{\mathbf{1}} & {\boldsymbol{\theta}_{\mathbf{2}}} & \boldsymbol{\theta}_{\mathbf{1}} & \boldsymbol{\theta}_{\mathbf{2}} \\ \hline 10^{\circ} & 8^{\circ} & 50^{\circ} & 35^{\circ} 0^{\prime} \\ 20^{\circ} & 15^{\circ} 30^{\prime} & 60^{\circ} & 40^{\circ} 30^{\prime} \\ 30^{\circ} & 22^{\circ} 30^{\circ} & 70^{\circ} & 45^{\circ} 30^{\prime} \\ 40^{\circ} & 29^{\circ} 0^{\prime} & 80^{\circ} & 50^{\circ} 0^{\prime} \\ \hline \end{array} $$

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)
Ptolemy, who lived in the city of Alexandria in Egypt during the second century $\mathrm{AD}$, gave the measured values in the following table for the angle of incidence $\theta_1$ and the angle of refraction $\theta_2$ for a light beam passing from air into water. Do these values agree with Snell's Law? If so, what index of refraction results? (These data are of interest as the oldest recorded physical measurements.)
$$
\begin{array}{|llll|}
\hline \boldsymbol{\theta}_{\mathbf{1}} & {\boldsymbol{\theta}_{\mathbf{2}}} & \boldsymbol{\theta}_{\mathbf{1}} & \boldsymbol{\theta}_{\mathbf{2}} \\
\hline 10^{\circ} & 8^{\circ} & 50^{\circ} & 35^{\circ} 0^{\prime} \\
20^{\circ} & 15^{\circ} 30^{\prime} & 60^{\circ} & 40^{\circ} 30^{\prime} \\
30^{\circ} & 22^{\circ} 30^{\circ} & 70^{\circ} & 45^{\circ} 30^{\prime} \\
40^{\circ} & 29^{\circ} 0^{\prime} & 80^{\circ} & 50^{\circ} 0^{\prime} \\
\hline
\end{array}
$$

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