Chapter 2.3, Problem 81E

(Modeling) Speed of Light When a light ray travels from one medium, such as air, to another medium, such as water or glass, the speed of the light changes, and the light ray is bent, or refracted, at the boundary between the two media. (This is why objects under water appear to be in a different position from where they really are.) It can be shown in physics that these changes are related by Snell's law

$\frac{c_1}{c_2}=\frac{\sin {\theta }_1}{\sin {\theta }_2},$

where c₁ is the speed of light in the first medium, c₂ is the speed of light in the second medium, and θ₁ and θ ₂ are the angles shown in the figure. In Exercises 81 and 82, assume that $c_1=3\times {10}^8$ m per sec.

Find the speed of light in the second medium for each of the following.

(a) ${\theta }_1={46}^{\circ },{\theta }_1={31}^{\circ }$

(b) ${\theta }_1={39}^{\circ },{\theta }_2={28}^{\circ }$