2016 Feb

The Physics Behind Rainbow Formation

March 7, 2016

Refraction and Reflection
Figure 1

Rainbow is a curve of hues formed in the sky in specific circumstances, created by the refraction and scattering of the daylight by rain or other water droplets in the sky. It can as well be defined as a meteorological wonder that is created by light reflection, refraction and scattering in water droplets, bringing about a spectrum of light. It takes the shape of a kaleidoscopic circular segment. A primary rainbow is a rainbow where the circular segment indicates violet at the inner side and red on the outer side. This rainbow is produced by light beam refraction upon entering a water droplet, then total internal reflection occurs inside the droplet and refracted once again as it leaves it, as shown in figure 1 above.

In a double rainbow, there is a second arc, appearing outside the primary arc, that has its colors’ order reversed, that is, violet is on the outer side of the arc. The deviation angle between the incidence light rays from the sun and the rays refracted towards the observer is about 420 for the red light. As learnt during our A Level Physics tuition classes, due to shorter wavelength, the blue light refracts more than the red light, its deviation angle from the initial sun rays is about 400. As shown in figure 2 below. The red light leaves the droplet at a steeper angle towards the ground. There are some paths by which the initial ray can pass through a water droplet and subsequent angle towards the earth. Some of these paths are dependent on the part of the water droplet which the incoming rays contact. Additional paths are dependent on the sun’s location in the sky and the following trajectory of the incidence rays into the droplet. The highest concentration of outgoing rays is at 400-420 deviation angles. At these angles, the light that has been dispersed is sufficiently bright to result in a rainbow appearance in the sky.

Double Rainbow

Figure 2

Formation of the rainbow’s second arc

The second arc is also referred to as the secondary rainbow. This rainbow is about 10° further out from the anti-solar point than the primary rainbow (figure 3).

Second Arc Formation
Figure 3

The secondary rainbow has its colors reversed and is about twice as wide as the primary. The region separating the two rainbows should be a bit darker than the sky outside the secondary rainbow. The sky outside a primary rainbow is darker than the sky inside the bow because, raindrops are spherical and disperses light over an entire annular disc in the atmosphere. The disc’s radius depends on the light wavelength, where the red light is dispersed over a greater angle than the blue light. Mostly, the dispersed light overlaps at all wavelengths. This results in white light that makes the sky brighter.

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