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whyin the formation of rainbow smallraindrops undergoes total internal reflaction

whyin the formation of rainbow  smallraindrops undergoes total internal reflaction


1 Answers

35 Points
6 years ago

A rainbow does not exist at one particular location. Many rainbows exist; however, only one can be seen depending on the particular observer's viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. This light is what constitutes the rainbow for that observer. The whole system composed by the sun's rays, the observer's head, and the (spherical) water drops has an axial symmetry around the axis through the observer's head and parallel to the sun's rays. This already explains the circular arc shape of the rainbow: whatever is the effect of any water's drop on the observer, rotating around the axis must leave it unchanged. Therefore, the bow appears to be centered on the shadow of the observer's head, or more exactly at the antisolar point (which is below the horizon during the daytime, unless the observer is sufficiently far above the earth's surface), and forms a circle at an angle of 40–42° to the line between the observer's head and its shadow. As a result, if the sun is higher than 42°, then the rainbow is below the horizon and usually cannot be seen as there are not usually sufficient raindrops between the horizon (that is: eye height) and the ground, to contribute.

The light at the back of the raindrop does not undergo total internal reflection, and some light does emerge from the back. However, light coming out the back of the raindrop does not create a rainbow between the observer and the sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow.[17]

The reason the returning light is most intense at about 42° is that this is a turning point – light hitting the outermost ring of the drop gets returned at less that 42°, as does the light hitting the drop nearer to its centre. There is a circular band of light that all gets returned right around 42°. If the sun were a laser emitting parallel, monochromatic rays, then the luminance (brightness) of the bow would tend toward infinity at this angle (ignoring interference effects). (See Caustic (optics).) But since the sun's luminance is finite and its rays are not all parallel (it covers about half a degree of the sky) the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its wavelength, and hence its colour. This effect is called dispersion. Blue light (shorter wavelength) is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside. The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. (A "rainbow" formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow.)

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°.[15] 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.[16]

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