11.1: Visible Light and Scattering

The Visible Spectrum

Recall the electromagnetic energy spectrum from Chapter 2, with the visible portion near the center between ultraviolet and infrared:

Figure \(\PageIndex{1}\): The electromagnetic energy spectrum highlights the wavelength of visible light. The visible spectrum spans wavelengths from approximately 400 to 700 nm. The shortest wavelengths appear violet and blue, while the longest wavelengths appear red. Wavelengths from 500 to 600 nm appear green and yellow/orange, respectively. (CC-BY-NC-ND 2.0; Scfiasco via Flickr).

Figure 11.1.1 is a diagram of the electromagnetic spectrum showing major categories of electromagnetic radiation arranged by wavelength. The diagram includes gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, radar, and radio waves. Wavelength values are shown on a scale in meters, ranging from extremely small to very large. A magnified section highlights the visible-light region of the electromagnetic spectrum, indicating that it occupies a narrow range within the broader spectrum and is typically measured in nanometers, from 400 to 700 nm. A breakdown of colors by wavelength is provided in Table 11.1.1.

Table \(\PageIndex{1}\): Visible Light Wavelength Ranges

Perceived Color	Approximate Wavelength Range (nanometers)
Violet	380–450 nm
Blue	450–495 nm
Green	495–570 nm
Yellow	570–590 nm
Orange	590–620 nm
Red	620–750 nm

Notice that blue and purple colors have a relatively short wavelength (~400 nm) and orange and red have a relatively long wavelength (~700 nm). While slight, this difference significantly alters how light interacts with particles in the atmosphere. Before we begin, let’s define a few key terms to help us understand the material that follows.

1. White light contains all colors. Sunlight is considered white light.
2. The color an object appears to be is due to the reflection of that color toward your eye. For example, a green leaf looks green because it absorbs red and blue light but reflects green light.

Based on this simple description, we can say that the sky appears blue because molecules in the atmosphere reflect blue light. But why do they reflect blue light more than red light? This concerns the relative sizes of the molecules and the wavelengths of light that interact with them. In general, there are three laws governing the interactions between wavelength and particles. We’ll define λ as the wavelength of light, and d as the diameter of the molecule or particle.

When the wavelength of light is much larger than the diameter of the molecule or particle, Rayleigh scattering is dominant.

\[\text { Rayleigh Scattering } \lambda \gg d \nonumber \]

When the wavelength of light is within an order or two of magnitude of the diameter of the molecule or particle, Mie scattering is dominant.

\[\text { Mie Scattering } \lambda \sim d \nonumber \]

Finally, when the wavelength of light is much smaller than the diameter of the molecule or particle, Geometric Optics is dominant.

\[\text { Geometric Optics } \lambda \ll d \nonumber \]

Rayleigh Scattering

Rayleigh scattering is the reason the sky is blue. Rayleigh scattering occurs when the wavelength of visible light is much larger than the particles it is interacting with. Such is the case with the tiny molecules in Earth’s atmosphere. The amount of scattering, “\(S\)”, is proportional to the fourth power of the wavelength of light.

\[S \sim \frac{1}{\lambda^4} \nonumber \]

Because this relationship is inversely proportional to wavelength (λ), shorter wavelengths are scattered more strongly. Purple and blue light have a shorter wavelength than orange and red light and are therefore scattered more, accounting for the blue color of Earth’s atmosphere.

Figure \(\PageIndex{2}\): During Rayleigh scattering, light is scattered close to uniformly off the object in all directions. Meanwhile, Mie scattering scatters light more strongly in the forward direction and exhibits a weaker wavelength dependence. (Public Domain; Shedding Light on PACE via NASA)

Mie Scattering

Mie scattering, on the other hand, is the reason clouds appear white. Mie scattering occurs when the wavelength of visible light is approximately the same as the particle or droplet diameter (within a factor of 10 or 100). When this is true, all wavelengths of visible light are scattered roughly equally. In this case, the illuminating color is the same as the reflecting color. In the case of clouds, they appear white because white light from the sun illuminates them. Figure \(\PageIndex{2}\) shows the difference between Rayleigh and Mie scattering.