Re: Why aren't the rays we see from the sun parallel?

Good question, Tim!

The rays that reach the earth from the sun are, as you noted, pretty parallel. An easy way to see how parallel they are is to notice that the diameter of the sun is about 830,000 miles and that they distance to the sun is about 93,000,000 miles -- I'd use metric distances, but the most accessible reference I have on solar diameter gave the distance in miles. The angle of the sun, as seen from the earth and measured in radians, is roughly given by dividing the diameter by the distance... When you do this, you find that the answer is about .009 radians, or about .5 degrees. So the angle between a light ray coming from one edge of the sun's disk will differ in angle from one coming from the other edge of the sun's disk by about half a degree.

[If you wanted to be exact in the computation, you could say that the angle is 2 X arctan ((Diameter/Distancer)/2)... but this gives .536 degrees, which is really the same answer. By the way, if you haven't noticed so far, most scientists are happy to use approximations which are accurate to one or two significant digits rather than carry things to five or six decimal places. This is because it usually makes no difference in terms of understanding the phenomena and avoids messy, meaningless numbers.]

This half-degree angle may not seem very small to you, if you expected light from the sun to be parallel, AND IT ISN'T! The reason is that the sun is a mighty big place. If the sun were a point source of light, on the other hand, the rays reaching your eyes would be equisitely parallel -- if the pupils in your eyes were open to about 1 mm, as they would be on a sunny day, the difference in the optical paths traversed by rays entering on the extreme edges of the pupils would vary by about 10 billionths of the wavelength of visible light. If you considered the path difference between light entering both eyes, the path differences would be about 1 millionth of the wavelength of visible light. All of these conclusions are nice, but they really point out a couple of things: (1) light from the sun isn't very parallel; (2) if you considered light from stars (many of which are about the same size as the sun but are 10,000 times or more distanct from the earth), the angles would be very tiny indeed... so that they do act pretty much like point sources and produce light which is to all extents and purposes parallel by the time we see it.

So far, we haven't even begun to answer your question, however...

While I don't know for absolute certain, I believe that the answer is the same as for most questions relating to what you see in the sky when the sun is shining: scattering. Scattering of light refers to the process whereby light interacts with matter -- sometimes dust, sometimes molecules -- and bounces off in a different direction. Scattering is, for example, what makes the sky blue when you look overhead: blue light is much more strongly scattered by air molecules than green or red light, so that when you look at light coming to you from other than in the exact direction of the sun, you'll see blue light coming at you. Scattering is also what makes sunsets on humid days look red: for the same reason as above, light transitting through a very long path in the atmosphere (as it does when we're looking over at the horizon) has most of its blue light and some its yellow light scattered out, leaving red light to reach us on earth.

Scattering is a pretty complicated process, actually, and depends on the size and composition of the scattering particles and the wavelength distribution of the incoming light. For the case that you're most interested in, I think that what you're seeing is light that is scattered one or more times in the forward direction from tiny particles (bigger than molecules, smaller than sand grains) in the air. What's probably happening is that these particles act as tiny marbles in the air, letting most of the light pass through at its 0.5 degree angle, reflecting a significant amount out at relatively small angles. This scattered light can be scattered again one or more times, but the intensity is reduced significantly each time. If you guess that each scattering center is a sphere, and you draw a little picture of light reflecting from it, you can probably convince yourself that this is possible -- but the math associated with trying to quantify this gets pretty messy.

What you can conclude pretty quickly, however, is that it's possible to get significant scattering angles -- 5 or 10 degrees seems reasonable -- and that you need enough centers to scatter light effectively without having so many that the atmosphere becomes opaque (like in a cloud). The most likely conditions to observe the phenomena you have observed are those when there's a considerable amount of aerosol water (teeny water droplets) in the air, either before or after a cloud has produced rain. Additionally, it helps to have a dark background -- which is often the case if thick cumulus clouds mask large portions of the sky... and since cumulus clouds are typically producers of thunderstorms, which require and generate large quantities of tiny water droplets, the phenomena you observed are often seen when this kind of cloud is around... at least in my experience.

It might be fun to try to duplicate the effect in the lab or at home. If you've got a laser pointer, it might be fun to put in in a bathroom and turn on the shower -- really hot, so that steamy water vapor slowly fills the room. If my arguments are reasonable, you should initially see the narrow beam and it should then broaden into a wider beam as the bathroom gets steamier. [Note: If you do this, be careful to make sure that the beam does not reflect off a mirror or any glass surfaces or go by any means into anyone's eyes. It probably would be best to aim the laser up at the ceiling and warn everyone around not to look directly down the beam. BE CAREFUL!]

Since it's about time for my morning shower, I think I'll try this myself!

Thanks for the question!
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