26.5

The Dispersion of Light: Prisms and Rainbows

Figure 26-18a shows a ray of monochromatic light passing through a glass prism surrounded by air. When the light enters the prism at the left face, the refracted ray is bent toward the normal, because the refractive index of glass is greater than that of air. When the light leaves the prism at the right face, it is refracted away from the normal. Thus, the net effect of the prism is to change the direction of the ray, causing it to bend downward upon entering the prism, and downward again upon leaving. Because the refractive index of the glass depends on wavelength (see Table 26-2), rays corresponding to different colors are bent by different amounts by the prism and depart traveling in different directions. The greater the index of refraction for a given color, the greater the bending, and part b of the drawing shows the refractions for the colors red and violet, which are at opposite ends of the visible spectrum. If a beam of sunlight, which contains all colors, is sent through the prism, the sunlight is separated into a spectrum of colors, as part c shows. The spreading of light into its color components is called dispersion.

Table 26-2 Indices of Refraction n of Crown Glass at Various Wavelengths

Approximate Color | Wavelength in Vacuum (nm) | Index of Refraction n
Red | 660 | 1.520
Orange | 610 | 1.522
Yellow | 580 | 1.523
Green | 550 | 1.526
Blue | 470 | 1.531
Violet | 410 | 1.538

Figure 26-18 (a) A ray of light is refracted as it passes through the prism. The prism is surrounded by air. (b) Two different colors are refracted by different amounts. For clarity, the amount of refraction has been exaggerated. (c) Sunlight is dispersed into its color components by this prism. (David Parker/Photo Researchers)

In Figure 26-18a the ray of light is refracted twice by a glass prism surrounded by air. Conceptual Example 8 explores what happens to the light when the prism is surrounded by materials other than air.

| Conceptual Example 8 | | | The Refraction of Light Depends on Two Refractive Indices

In Figure 26-18a the glass prism is surrounded by air and bends the ray of light downward. It is also possible for the prism to bend the ray upward, as in Figure 26-19a, or to not bend the ray at all, as in part b of the drawing. How can the situations illustrated in Figure 26-19 arise?

Figure 26-19 A ray of light passes through identical prisms, each surrounded by a different fluid. The ray of light is (a) refracted upward and (b) not refracted at all.

Reasoning and Solution Snell’s law of refraction includes the refractive indices of both materials on either side of an interface. With this in mind, we note that the ray bends upward, or away from the normal, as it enters the prism in Figure 26-19a. A ray bends away from the normal when it travels from a medium with a larger refractive index into a medium with a smaller refractive index. When the ray leaves the prism, it again bends upward, which is toward the normal at the point of exit. A ray bends toward the normal when traveling from a smaller toward a larger refractive index. Thus, the situation in Figure 26-19a could arise if the prism were immersed in a fluid, such as carbon disulfide, which has a larger refractive index than does glass (see Table 26-1).
We have seen in Figures 26-18a and 26-19a that a glass prism can bend a ray of light either downward or upward, depending on whether the surrounding fluid has a smaller or larger index of refraction than the glass. It seems logical to conclude, then, that a prism will not bend a ray at all, neither up nor down, if the surrounding fluid has the same index of refraction as the glass—a condition known as index matching. This is exactly what is happening in Figure 26-19b, where the ray proceeds straight through the prism as if it were not even there. If the index of refraction of the surrounding fluid equals that of the glass prism, then , and Snell’s law reduces to . Therefore, the angle of refraction equals the angle of incidence, and no bending of the light occurs.
Related Homework: Conceptual Questions 17, 20; Problems 42, 108

Check Your Understanding 3

Two blocks, made from the same transparent material, are immersed in different liquids. A ray of light strikes each block at the same angle of incidence. From the drawing, determine which liquid has the greater index of refraction. (The answer is given at the end of the book.)

Background: When a ray of light is refracted at the interface between two materials, the change in direction of the ray depends on the refractive indices of both materials, according to Snell’s law of refraction.
For similar questions (including calculational counterparts), consult Self-Assessment Test 26.1, which is described at the end of this section.

Another example of dispersion occurs in rainbows, in which refraction by water droplets gives rise to the colors. You can often see a rainbow just as a storm is leaving, if you look at the departing rain with the sun at your back. When light from the sun enters a spherical raindrop, as in Figure 26-20, light of each color is refracted or bent by an amount that depends on the refractive index of water for that wavelength. After reflection from the back surface of the droplet, the different colors are again refracted as they reenter the air. Although each droplet disperses the light into its full spectrum of colors, the observer in Figure 26-21a sees only one color of light coming from any given droplet, since only one color travels in the right direction to reach the observer’s eyes. However, all colors are visible in a rainbow (see Figure 26-21b) because each color originates from different droplets at different angles of elevation.

Figure 26-20 When sunlight emerges from a water droplet, the light is dispersed into its constituent colors, of which only two are shown.

Figure 26-21 (a) The different colors seen in a rainbow originate from water droplets at different angles of elevation. (b) A couple is standing by a rainbow at the foot of a waterfall. (Eric Bean/The Image Bank/Getty Images)

The physics of rainbows.

Test your understanding of the material in Sections 26.1, 26.2, 26.3, 26.4 and 25.5 :

· | The Index of Refraction
· | Total Internal Reflection
· | The Dispersion of Light
· | Snell’s Law and the Refraction of Light
· | Polarization and the Reflection and Refraction of Light

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.