11.2: Visibility

Geometric Optics

Finally, geometric optics explains rainbows by tracing a beam of light, called a ray. Unlike scattering, geometric optics is used only when the size of the objects interacting with light is orders of magnitude larger than the wavelength, e.g., raindrops. Tracing a ray of light as it passes through a raindrop helps us understand how and why rainbows form. When light encounters an interface between two media, such as air and water, it can reflect or refract. Refraction is responsible for everyday conundrums, as in Figure 11.2.1.

Figure \(\PageIndex{1}\): Glass filled with water placed on a flat surface outdoors. A pen is partially immersed in the water at an angle. The portion of the rod submerged in water appears displaced relative to the portion above the surface, illustrating how light refracts when it passes from air into water. (CC-BY-NC 2.0, Martin LaBar via Flickr).

Refraction occurs when rays bend at an interface between two media. Reflection occurs when rays bounce back from an object. These two phenomena are responsible for atmospheric optical phenomena such as rainbows, halos, and sundogs. Here, we focus solely on rainbows, the geometric optics observed in liquid raindrops.

Figure \(\PageIndex{2}\): Diagram showing angle of incidence, reflection, and refraction of a ray of light. (Public Domain; Nilock, via Wikimedia Commons). Alternative Description of Image.

Figure 11.2.2 shows a light ray incident on an interface between two media with different refractive indices, such as air and water. In this case, some of the incoming (incident) light will either refract from the air into the water, reflect back into the air, or be absorbed into heat. In the case of light interacting with a raindrop, we observe a combination of refraction and reflection. A single rainbow has two refractions and one reflection, and the second rainbow seen in a double rainbow has two refractions and two reflections.

The top right image of Figure 11.1.3 shows the interaction of light with a raindrop responsible for a single rainbow. Light comes in contact with a rain drop, refracts as it enters the rain drop, reflects off the back side of the rain drop, and refracts again as it exits the rain drop. The two refractions split the colors of light, as a prism does. This is because the refractive index of light depends on wavelength; shorter wavelengths refract more strongly than longer wavelengths.

Figure \(\PageIndex{3}\): The formation of a rainbow with light propagation. Legend: 1.) Spherical droplet 2.) Places where internal reflection of the light occurs 3.) Primary rainbow 4.) Places where refraction of the light occurs 5.) Secondary rainbow 6.) Incoming beams of white light 7.) Path of light contributing to the primary rainbow 8.) Path of light contributing to secondary rainbow 9.) Observer 10.) Region forming the primary rainbow 11.) Region forming the secondary rainbow 12.) Zone in the atmosphere holding countless tiny spherical droplets (CC-BY-SA 3.0; Peo, via Wikimedia Commons). Alternative Description of Image.

Put concisely, a rainbow is an atmospheric phenomenon displaying a spectrum of light as a result of the refraction of light in water droplets. This is possible because the wavelength of light is much smaller than the size of the raindrop. Primary rainbows have red on the outside of the circle and purple on the inside. There is always a 42° angle between the incident light, the primary rainbow, and the observer. This constant angle is shown in Figure 11.1.3. At a given time, rainbows appear different to different observers because of different interactions between incoming light rays and water droplets. For instance, one observer may see a well-defined rainbow in an area of large raindrops and bright sun. Another observer half a kilometer away with smaller raindrops may see a partial rainbow.

Secondary rainbows are outer rainbows with red on the inside of the circle and purple on the outside because of the double reflection. Secondary rainbows occur at a 52° angle; secondary rainbows are higher than primary rainbows (Figure 11.1.4). They’re not as bright as primary rainbows, also because of the double reflection. Triple rainbows are also possible and have been observed, but are much less frequent.

Figure \(\PageIndex{4}\): Double rainbow in a stormy sky. Notice how the colors are flipped in the two rainbows, and how the secondary rainbow is not as bright as the primary rainbow (CC-BY-SA 4.0; Shintaro Russell via Atmospheric Processes and Phenomena).

How to see Rainbows

The best chance of seeing a rainbow is when there is rain and sun low in the sky at the same time. An observer may see a rainbow if the sun is behind them and they are facing a region of rain. As the sun lowers in the sky, the height of the rainbow will increase because of the constant 42° angle. Rainbows cannot be seen on the ground at noon because a 42° angle is not possible. Rainbows appear as half arcs only because the ground typically blocks the other half. Rainbows are common in Hawai’i due to abundant sunlight and frequent rainfall.

Visibility

Visibility is the final topic on the interaction of light with particles in Earth’s atmosphere covered in this chapter. In general, the topic of visibility is simply a question of what can be seen and how far away it is. When someone says that the visibility today is 10 miles, it means that one can see objects 10 miles away. In the Arctic, where the air is extremely dry and clean, visibility of 100 miles (161 km) is common. On the other hand, when you cannot see objects 100 meters (~330 ft) away, this is referred to as zero visibility. As you may imagine, visibility is extremely important for pilots and drivers. Fog in the atmosphere provides the worst conditions for visibility. Figure 11.2.5 shows the Great Smoky Mountains along the Tennessee–North Carolina border in the southeastern United States. The trees in the foreground are nearly clear, but with each additional ridge, the mountainside appears increasingly white. We assume that each ridge has the same type of foliage as the first. This indicates that objects farther away appear brighter or hazier.

Figure \(\PageIndex{5}\): A photo from the Great Smoky Mountains National Park illustrating that objects far away appear hazier. (CC-BY 2.0; Dave Ynin via Flickr).

The change in brightness is attributable to particulate matter in the atmosphere. This can come in the form of aerosols or hydrometeors (cloud droplets, raindrops, snowflakes, etc.). In the case of the mountain image above, the Great Smoky Mountains are known for emitting plentiful volatile organic compounds (VOCs) that act as cloud condensation nuclei (CCN) and produce clouds near ground level (i.e., low-hanging fog). Both the aerosols and the hydrometeors reduce visibility.

Many believe that a lack of visibility is caused by objects blocking your view. However, if that were the case, the background would appear darker. Instead, a lack of visibility is caused by objects scattering light towards your eye. With greater distances, your eye has to look through a larger portion of the atmosphere and, therefore, more opportunity for light to scatter towards you. The scattered light appears white because Mie scattering is occurring. Figure 11.2.6 presents an image of the same scene on a clear and polluted day in Sequoia and Kings Canyon National Park.

Figure \(\PageIndex{6}\): A clear (top) and polluted (bottom) day at Sequoia & Kings Canyon National Park. (Public Domain; National Park Service).

This national park is often affected by pollution from the Central Valley of California. On polluted days, more aerosols and particulate matter are in the atmosphere, so more particles are available to scatter light toward your eye. Scene details are lost, and the mountains in the distance can’t be seen at all. The visible range is shorter in the bottom image than in the top.