Rainbow Shape
Why does
the light that is dispersed by the rainbow forms a bow? The answer
involves the use of some simple geometry. The first point is that a
rainbow is not a two-dimensional arc; it is in fact a three
dimensional cone with the apex at the observer's eye. The reason that
it appears to be only a two dimensional flat object isbecause there
is no evidence of distance. All the drops, which disperse
lighttowards the observer to form the rainbow, lie in the shape of a
cone withmany different layers. The outside layers disperse the red
component, thelayer below that - the orange component, and the
layer below that -the yellow component, etc.
Consider the path of a ray of monochromatic light through a single spherical raindrop. Imagine how light is refracted as it enters the raindrop, then how it is reflected by the internal, curved, mirror-like surface of the raindrop, and finally how it is refracted as it emerges from the drop. If we then apply the results for a single raindrop to a whole collection in the sky, we can visualize the shape of the bow.
Figure 3. Source:
http://www.unidata.ucar.edu/staff/blynds/rnbw4.gif
Also consider only the dispersion of the red component of the light. It has been shown previously that the red component is seen when the angle between the incident rays and dispersed rays make an angle of 42 degrees. Of course beams are dispersed at 42 degrees from drops all over the sky in all directions up, down, left, and right. However, only red light, which reached the observer eye, comes from the water drops which are on the cone with sideto axis angle of 42 degrees. If the observer's eye is at the apex of the coneas shown in Figure 3, then to see the violet part of the bow we would needto look at 40 degree to the conical axis. Therefore, the cone that producesthe violet component comes from a cone inside that of the cone which producedthe red part. The same argument can be made for all the other colors, andbecause different colors are formed by different cones, when they are viewedfrom the apex they appear in the form of a bow.
It is interesting to note that because only the drops on the cone with apex at the observer's eye are responsible for the formation of the rainbow, which an observers sees, then an important implication is that each person looking at a different rainbow. That leads to another interesting fact that both of the observer's eyes actually see a different rainbow, as they are both at the apex of different cones.
Consider the path of a ray of monochromatic light through a single spherical raindrop. Imagine how light is refracted as it enters the raindrop, then how it is reflected by the internal, curved, mirror-like surface of the raindrop, and finally how it is refracted as it emerges from the drop. If we then apply the results for a single raindrop to a whole collection in the sky, we can visualize the shape of the bow.
Figure 3. Source:
http://www.unidata.ucar.edu/staff/blynds/rnbw4.gif
Also consider only the dispersion of the red component of the light. It has been shown previously that the red component is seen when the angle between the incident rays and dispersed rays make an angle of 42 degrees. Of course beams are dispersed at 42 degrees from drops all over the sky in all directions up, down, left, and right. However, only red light, which reached the observer eye, comes from the water drops which are on the cone with sideto axis angle of 42 degrees. If the observer's eye is at the apex of the coneas shown in Figure 3, then to see the violet part of the bow we would needto look at 40 degree to the conical axis. Therefore, the cone that producesthe violet component comes from a cone inside that of the cone which producedthe red part. The same argument can be made for all the other colors, andbecause different colors are formed by different cones, when they are viewedfrom the apex they appear in the form of a bow.
It is interesting to note that because only the drops on the cone with apex at the observer's eye are responsible for the formation of the rainbow, which an observers sees, then an important implication is that each person looking at a different rainbow. That leads to another interesting fact that both of the observer's eyes actually see a different rainbow, as they are both at the apex of different cones.
