phy1020.DVI

Chapter 57

The Rainbow

Therainbow, one of the most beautiful and striking objects seen in Nature, is typically visible during a late
afternoon rain shower, when the Sun is low in the sky and shining at the same time (Fig. 57.1). Understanding
all of the features of the rainbow requires many different ideas from optics.

57.1 Colors

The most obvious feature of the rainbow is its selection of colors. The phenomenon responsible for the colors
isdispersion(Chapter 54). White light from the Sun enters each raindrop, refracts into the interior of the drop,
reflects once via total internal reflection, and refracts back out of the drop again. The angles of refraction are
determined by Snell’s law and the index of refraction. But because of dispersion, the index of refraction (and
therefore the angle of refraction) is different for each color of light (Table 57-1).

Table 57-1. Indices of refraction of water for different colors.

Color Wavelength (nm) nwater

Red 650 1.3317

Orange 590 1.3333

Yellow 570 1.3340

Green 510 1.3364

Blue 475 1.3381

Indigo 445 1.3400

Violet 400 1.3436

When you see a rainbow in Nature, you can often seetwobows: a brightprimary rainbow, and above it a
faintersecondary rainbow(Fig. 49.1). The secondary bow is due to light reflecting a second time inside the
raindrop due to total internal reflection.

57.2 The Primary Rainbow

In the brighter primary rainbow, red appears on the outside edge and violet on the inside edge.^1 The primary
rainbow is due to light reflecting a single time inside the raindrops due to total internal reflection.

(^1) The next time you see a drawing of a rainbow, check to see whether the artist put the colors in the correct order, with red on the
outside edge. Drawings have the colors wrong as often as not.