Chapter 22, Problem 58RPP

Rainbows How is a rainbow formed? Recall that the index of refraction of a medium is slightly different for different colors. When white light from the Sun enters a spherical raindrop, as shown in Figure 22.25, the light is refracted, or bent. After reflecting off the back surface of the drop, the light is refracted again as it leaves the front surface.

Each drop separates the colors of light. An observer on the ground with her back to the Sun sees at most one color of light coming from a particular drop (see Figure 22.26). If the observer sees rod light from a drop (for example the top drop in Figure 22.26), the violet light for that same drop is deflected above her head However, if she sees violet light coming from a drop lower in the sky the red light from that drop is deflected below her eyes onto the ground. She sees red light when her line of view makes an angle of $42°$ with the beam of sunlight and violet light when the angle is $40°$. Other colors of light are seen at intermediate angles.

58 Suppose that light entered one side of a square water droplet of refractive index 1.33 at an incident angle of $15°$

Some of the light reflects off the back surface and then goes back out on the same side as it entered What is the angle of refraction of light leaving the square droplet?

$\begin{array}{l}\text{a}\text{. 15°}\hfill \\ \text{b}\text{. 18°}\hfill \\ \text{c}\text{. 20°}\hfill \\ \begin{array}{l}\text{d}\text{. 24°}\\ \text{e}\text{. 35°}\end{array}\hfill \end{array}$