Chapter 1, Problem 13PS

Refraction When you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is $\mathrm{1.333.}$ This is the ratio of the sine of ${\theta }_1$ and the sine of ${\theta }_2$ (see figure).

(a) While standing in water that is $2$ feet deep, you look at a rock at angle ${\theta }_1=60°$ (measured from a line perpendicular to the surface of the water). Find ${\theta }_2$.

(b) Find the distances $x$ and $y.$

(c) Find the distance $d$ between where the rock is and where it appears to be.

(d) What happens to $d$ as you move closer to the rock? Explain.