God Bless
Jonathan
David Bowman wrote:
> I hope this thread's principals don't mind me interjecting myself here,
> but I wanted to pick a nit regarding rainbow optics being motivated by
> Jonathan's comment below, and to take the opportunity to explain more
> fully the conditions necessary for rainbows to be seen. Jonathan wrote:
>
> >With respect to rainbows they form every time white light passes though
> >airborne water droplets.
>
> Actually this is not correct. If it was, we would see a rainbow every
> time we looked up in the direction of the sun when it is hidden behind
> clouds. We don't.
>
> First of all 'water droplets' have nothing to do with rainbow formation.
> The kind of piece of water necessary to make a rainbow is the *drop* --
> not droplet. Droplets are much smaller than drops since typical droplets
> as in clouds tend to have sizes on the order of microns, whereas drops
> tend to have sizes on the order of millimeters. Drops exist when rain is
> falling. Droplets exist when clouds are present. In order for for a
> rainbow to exist the sunlight must interact with round transparent
> objects much larger than the range of wavelengths contained in the light
> in order for the geometric (i.e. ray) optics limit to hold, and so that
> diffraction effects become negligible. Water droplets are so small that
> their size is close enough to that of the light's wavelengths that
> diffraction effects are significant, ray optics doesn't accurately
> describe the situation properly, and the interaction between the droplets
> and the light is dominated by a scattering process called Mie scattering.
> In this process all the wavelengths of the sunlight are effectively
> scattered widely from each droplet over all possible angles relative to
> the direction of the incident sunlight. The result of all this Mie
> scattering is that the batch of droplets illuminated by a white light
> source looks *white*, i.e. like a cloud (not like a rainbow).
>
> The conditions necessary for a rainbow are: 1. A batch of spherical (or
> nearly spherical) scattering centers made of a substance that is
> transparent to white light but whose index of refraction is both
> significantly larger than 1 and is dispersive over the visible wavelength
> band (water does a good job meeting this requirement) exists and the
> typical intersphere distance is relatively large compared to the sphere
> diameters, and the spheres are distributed approximately randomly
> throughout the batch. 2. The size of the spheres must be so large
> compared to the wavelengths in the incident light that the laws of
> geometric optics hold (i.e. a ray description is valid and those rays
> obey the equal angles of incidence and reflection law for reflection from
> the spherical surfaces, and obey Snell's law for refraction across the
> interface between the interior of the sphere and the outside air). 3. The
> white light source must be directionally localized as an effectively
> point source of light. 4. The observer's point of view must be such that
> the observer looks at the batch of spheres from approximately the same
> side as the direction of the incident light but the viewing direction to
> the batch of spheres must satisfy a constraint where the line connecting
> the illumination source with the part of the batch of spheres that the
> observer is observing (when viewing a section of the bow) must make a
> correct angle (i.e. about 42 degrees for rainbows from water spheres)
> with the line connecting the same observed part of the batch of spheres
> to the observer. 5. The angle subtended by the whole illuminated batch
> of spheres at the location of the observer must be large enough so that a
> significant fraction of the arc of the circular bow can be seen for it to
> appear as a bow, 6. The background behind the batch of spheres must be
> dark enough.
>
> If these conditions are not all met a bow is not visible. These
> conditions *can* be met when it rains (on relatively rare occasions), and
> when a spray of drops is thrown into the air from various sources such as
> garden hoses, waterfalls, sea spray, geysers, fountains, etc. Drops of
> water tend to automatically satisfy condition 1. because of the optical
> properties of water and because surface tension tends to shape the drops
> into the necessary spherical shape. The drops can't be too large in size
> either since then the force of air resistence on their underside as they
> fall through the air causes them to have a flattened bottom side thus
> destroying the necessary spherical shape. Droplets (as in clouds) don't
> work because they are too small to satisfy condition 2.. Condition 3. is
> met when the sun is shining and not met when the sky is overcast. This
> creates a problem for observing *rain*bows because there is a strong
> tendency towards being overcast when it rains. Also, as a consequence of
> condition 4. the sun can't be any higher in the sky than 42 degrees above
> the horizon in order for at least some of the rainbow to appear above the
> horizon. Since the rain in the air tends to be seen above the horizon
> this tends to limit the times of rainbow viewing (for real rain) to the
> hours just after sunrise or just before sunset in order for a significant
> fraction of the rainbow circle to appear above the horizon so it can be
> visible. If it is possible to view the raindrops as well below the
> horizon (as when they are viewed from above from an airplane, then it may
> be possible to see the whole rainbow as a complete circle centered on the
> direction directly opposite the sun.
>
> > I have seen them in sea spray, water falls, and in
> >condensing water round hot springs. ....
>
> Yes, they can be visible with drops from these sources, but in all cases
> the rainbow is visible because of round *drops* in the air, not droplets.
>
> David Bowman
> dbowman@georgetowncollege.edu