Physics Paper on What Causes a Rainbow?
Rainbows occur due to the refraction, dispersion and reflection of sunlight by water droplets in the atmosphere, resulting in a spectrum of light (Myers 161). The spectrum forms an arc of seven colors across the sky, occurring directly across from the sun. Therefore, if the sun is in the east, a rainbow will form in the west, and vice versa. Rainbows are not located at specific distances from an observer’s position; rather, they are optical illusions. Apart from rain, a rainbow can also be formed in the presence of other water droplets in the air, such as mist, sprayed water and airborne dew.
Starting from the outside, the colors of a primary rainbow are red, orange, yellow, green, blue, indigo and violet. However, double rainbows can occur, which have both primary and secondary arcs. In a secondary arc, the colors are reversed with violet as the top color and red as the inner-most color. It is farther from the anti-solar point, and is bigger than and positioned above the primary rainbow.
The Visibility of a Rainbow
Rainbows are observed when there are water droplets in the atmosphere and the sunlight is at a low altitude behind the observer (Avison 80). As result, rainbows can only be seen in the western horizons during the morning and eastern horizons during early evenings. The most vivid rainbow can be seen when the clouds are partially dark and the observer is in a clear spot, in the direction of the sun. From the clear spot, one can see a perfect rainbow. Under such good visual clarity, the secondary rainbow is also clear. Rainbow effects are also present at waterfalls and water fountains, where water droplets are in the atmosphere. Rainbows can also be artificially created by spraying water in the air when it is sunny. The sky enclosed within a rainbow is bright, while that outside is a bit dull.
The anti-solar point is an imaginary point on the earth, directly opposite the sun from the observer’s viewpoint, where a rainbow is seen (Avison 83). The rainbow is an illusion, and its imagined position is known as an anti-solar point. When the sun is in the opposite direction above the horizon, the anti-solar point can be found below the horizon. The anti-solar point does not have a fixed position, as it varies with the observer’s position. Every observer has an anti-solar point, and it varies with changes in the observer’s position.
A rainbow occurs when sun rays pass through water droplets. Some of the light is reflected back, while the remaining enters the water droplet. Inside the water droplet, the light is refracted to the surface of the water droplet. Part of this refracted light is internally reflected off the back surface, and the remainder is refracted as it exits the droplet. The incoming light is reflected at an angle ranging between 00 and 420 (Myers 161). The angle of reflection depends on the refractive index of the water droplet, and not the size of the water droplet. Rainwater has a lower reflective index than sea water. Therefore, the rainbow radius created by a sea droplet is smaller than that of a rainwater droplet. The colors of a rainbow are determined by the wave length of the refracted light. This effect is commonly known as dispersion of light. Because blue light has a short wave length, when entering a raindrop, it is refracted at a greater angle. However, the reflection of light off the back of the droplet causes the blue light to emerge at a smaller angle.
Due to the refractive index of water, the light leaving the water droplet has its greatest intensity between 400 and 420, with respect to the incoming rays of sunlight (Katz 1035). The former characterizes the maximum intensity for violet light, while the latter is for red light. The other colors of the spectrum are intensified at angles between 400 and 420 (Katz 1035). The dispersion at different angles produces an arched rainbow. Since an observer only sees the colors coming from a specific location, different colors are viewed from different raindrops, at different elevations. The red color comes from droplets at higher elevations, while other colors come from droplets at lower elevations. Both refraction and dispersion are responsible for rainbows. The amount of scattering of light is proportional to its wave length. The scattering of sunlight molecules in the atmosphere is referred to as Raleigh scattering. Violet is scattered through greater angles, with more intensity. Violet light is scattered approximately 10 times more than red light (Katz 1035).
There are several types of rainbows, and each is defined by its different characteristics. Secondary types of rainbows result from the double reflection of light inside a droplet. Secondary rainbows are centered on the sun and are approximately 1300 red and 1270 violet wide (Serway 1134). The secondary rainbow always positions itself above the primary rainbow and its colors appear reversed, due to the reflection. A secondary rainbow appears more blurred than the primary rainbow, because less light escapes during the double reflection that results in its formation. The Alexander’s band is the shadowy area between a primary and secondary rainbow. In contrast with secondary rainbows, twinned rainbows appear when two separate rainbows join at the arc, to form one rainbow. Colors in the twinned rainbow appear in the same order with red as the outer color (Serway 1134).
After spraying water droplets into the air, I discovered that the rainbow only formed when the sun was behind me. The rainbow that formed had an array of colors with red at the top and violet on the inside. The colors that lay in between, from outwards to inwards, were orange, yellow, green, blue and indigo respectively (Gary 193). When I sprayed the droplets towards the sun, a rainbow did not form. The experiment was conducted during sunset, and thus, my back was towards the sun. The anti-solar point was directly opposite the sun, from my viewpoint. It lay above the horizon, when the sun was below it. The anti-solar point was located at the shadow of my head and moved as I changed positions.
Discussion of Results
The rainbow is seen only when there are water droplets in the atmosphere and the sun is behind you. Sometimes you may see a second rainbow above the first, with the colors in reverse order. Since the index of refraction depends on the color of the light, red light is not bent as much as violet light. The red ray strikes the back of each droplet at a point slightly above where the violet ray strikes it. When the rays reach the near side of the droplet, they are refracted again as they leave the water and enter the air. The second rainbow colors are reversed, because two reflections take place inside each droplet. Elevation also plays a role, with violet light being seen from the lower droplets and red light from the highest droplets.
A rainbow is always formed in the direction opposite to that of the sun. It is a beautiful natural phenomenon, that is common where there are water droplets in the atmosphere. However, a rainbow can also be artificially made by spraying water in the air in the presence of sunlight. To see a rainbow, you must have the sun behind you, as you look towards the sky. The water droplets over the cloud act like small prisms. When light from the sun enters a round shaped water molecule, the light is both refracted and dispersed, resulting in a rainbow. The different colors of light are bent through different angles. Inside the droplet, the different colors are reflected internally. The drop finally refracts the different colors of the light again when it comes out of the raindrop. These different colors of light, after leaving the raindrop, reach the observer’s eye. The point where the rainbow forms is known at the ant-solar point. This point does not have a fixed position, and varies based on the position of the observer. The rainbow is not an object, and therefore, the anti-solar point is an illusion that can not be reached.
Avison, John. The World of Physics. Cheltenham: Nelson, 1989.
Gary, Waldman. Introduction to Light: The Physics of Light, Vision, and Color, 2002.
Katz, Deborah M. Physics for Scientists and Engineers: Foundations and Connections, Extended Version with Modern. Cengage Learning, 2015.
Myers, Richard L. The Basics of Physics. Westport, Conn.: Greenwood, 2006.
Serway, Raymond A. Physics for Scientists and Engineers, Volume 2, Technology Update. Cengage Learning, 2015.