Rainbow and double rainbows explained with science

A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky.

It takes the form of a multicolored arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be full circles; however, the average observer sees only an arc formed by illuminated droplets above the ground, and centered on a line from the sun to the observer’s eye.

In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.

In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, with red on the inner side of the arc.

A rainbow is not located at a specific distance from the observer, but comes from an optical illusion caused by any water droplets viewed from a certain angle relative to a light source. Thus, a rainbow is not an object and cannot be physically approached. Indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems “under” or “at the end of” a rainbow, as seen by the first observer.

Rainbows span a continuous spectrum of colors. Any distinct bands perceived are an artifact of human . Color vision, and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side.

For colors seen by the human eye, the most commonly cited and remembered sequence is Newton’s seven fold red, orange, yellow, green, blue, indigo and violet, remembered by the mnemonic, Richard Of York Gave Battle In Vain (ROYGBIV).

Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew. Visibility Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle.

Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening. The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the sun. The result is a luminous rainbow that contrasts with the darkened background.

During such good visibility conditions, the larger but fainter secondary rainbow is often visible. It appears about 10° outside of the primary rainbow, with inverse order of colors. Explanation Light rays enter a raindrop from one direction (typically a straight line from the sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. The light leaving the rainbow is spread over a wide angle, with a maximum intensity at the angles 40.89–42°. (Note: Between 2 and 100% of the light is reflected at each of the three surfaces encountered, depending on the angle of incidence.

This diagram only shows the paths relevant to the rainbow.) White light separates into different colours on entering the raindrop due to dispersion, causing red light to be refracted less than blue light. When sunlight encounters a raindrop, part is reflected but part enters, being refracted at the surface of the raindrop. When this light hits the back of the drop, some of it is reflected off the back.

When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop. (The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow.) The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°.

This angle is independent of the size of the drop, but does depend on its refractive index. Seawater has a higher refractive index than rain water, so the radius of a “rainbow” in sea spray is smaller than a true rainbow. This is visible to the naked eye by a misalignment of these bows.