Why do sun rays fan out when you see them streaming through clouds? It makes it seem as if the light source is very close.
It’s all perspective. It’s just like railroad tracks seem to fan out from infinity. The sun’s rays do the same thing. It just that the rays are further apart.
Huygen’s principle states the every point on a wavefront is a source point for a secondary wavefront that, as with its parent wavefront, spherically diverges in a uniform medium. The new wavefront is a surface tangent to the surfaces of all of the secondary wavelets.
Diffraction is a “bending of light around an obstacle” that is observed when one is dealing with a limited portion of a wavefront. It can get more complicated. Try this: if you have a desk lamp hold your finger just above the desk top and note its shadow. Then watch what happens to that shadow as you raise your finger away from the desktop. Same thing that’s happening with sunlight passing through a hole in an overcast. Or, if your more ambitious, punch a hole in an opaque piece of paper to better simulate a hole in a cloud cover.
If you’re referring to the fact that the shadow gets fuzzy around the edges, that’s not primarily due to diffraction. The main effect here is that the light bulb (or the Sun, if you do it outside) is not a point source of light, so you get an umbra and a penumbra. In other words, around the edges of the shadow, your finger is only blocking the light from a portion of the bulb.
Chronos is right. Beatle, diffraction occurs when the opening is on the order of the size of the wavelength of the waves passing through. Visible light’s wavelengths are from 380 - 700 nm, far tinier than holes in the clouds.
We’re not talking about wavelength, rather a wavefront, which can be of infinite size (well, no bigger than the universe, I suppose).
In the example given, you don’t have a point source of light. Thus you don’t observe diffraction patterns on the ground (or desktop) because all of the diffraction patterns from many incoherent sources are overlapping. The penumbra is the mass gathering of diffraction patterns. It is diffraction that gets the light “around the corner”, so to speak. Skip the finger and stick with the hole in an opaque piece of paper.
Have you ever noticed the sun’s rays on the waters in the morning? (I guess it would be the same at sunset, but I run along the coast in the morning.) The water reflects the sun, but in rays. I can see the whole sunrise if I look at it, but if I look at the water, I see rays. I guess that’s just the reflection of the sun’s rays through clouds.
<b>zwaldd</b>
Dr. Matrix has the answer to your question, as I understand it. Stand between the 2x4s of the walls of a house being constructed and look up–they look like they fan out close to you, but you know they’re all parallel.
<b>beatle</b>
I’m speechless.
RM Mentock, I swear, I’m trying to understand what you meant.
A little help, perhaps (for us dummies)?
beatle, I think RM Mentock is trying to say that he’s speechless about your attempts to answer this question, but he’s being somewhat polite. Your explanations are extremely heavy on the wave-nature-of-light terminology, but what you’re saying (if I can figure it out) doesn’t hold up. No need to invoke Huygen’s Principle here - the rays appear to diverge in the clouds because you’re witnessing parallel lines going off in the distance, and they appear to converge towards a vanishing point.
Also, the penumbra of shadows cast by the sun are not partially lit because they’re diffracted around the edge of an object, but because only a portion of the sun is lighting them up. If you’re ever in a total eclipse, at the moment when the sun is just a tiny speck of light on one end of the moon, shadows will be sharp, because they’re from a point source of light.
I’m not convinced I’m wrong, but I’m certainly willing to learn.
So, go ahead and explain the fanning of the sunbeams to me in the absence of diffraction.
The original post is asking why you can see light and dark streaks in the sky an sunset, which converge towards the Sun. Apparently, zwaldd was thinking that the rays should be parallel, since their origin is the Sun, but the don’t look parallel.
The streaks are shadows of far-away clouds, so the air nearer to you is not being lit up by the Sun at those places. And they are parallel, but you’re looking at them going off in the distance towards the Sun, so they appear to converge into a vanishing point, just like when you look down railroad tracks. I’ve read that under the right circumstances, you can look away from the sunset and see the streaks continuing into the distance, and guess what? They appear to converge to a point opposite the Sun, as you would logically expect, but it would sure look wierd.
I don’t think Dr. Matrix’s answer is right. Parallel lines that start close to the observer meet at the horizon or the ‘vanishing point’ in the distance. The light rays you see through the clouds fan very sharply, and if you continued the lines, they would meet far short of the sun. If you stood parallel lines on end, far away from you, like the sun’s rays, you would not see such a sharp vanishing effect. For example, if you stood right below the twin towers of the World Trade Center, you would see the lines draw closer together towards the top. However, if you looked at the towers from a short distance, like the light rays coming through clouds in the distance, you would not see such a vanishing effect. You would still see the lines as parallel.
CurtC
No, I’m not talking about a sunset. You’d be right about a sunset. I’m talking about nearby clouds in the middle of the day, where you see the light rays going up, not forward as you would at dusk.
Actually, he is 
This is perspective, linked with the fact that we see the sky as curved. These combine in unusual ways.
For example, on a particularly hazy or dusty day, you can actually see the rays of light converging on the opposite side of the sky. This proves the point: they start at the Sun, diverge to maximum separation above your head, and reconverge 180 degrees around the horizon from the Sun. I have seen this effect five or six times, and it is very striking.
These kinds of rays are called crepuscular, so I can say with confidence that I have seen crepuscular rays converging on the anti-solar apex. I have more about this on my very own website: Phil Plait's Bad Astronomy: Bad News
And sorry, I make the same joke there.
beatle, I apologize.
Here is a link to an Exploratorium illustration of the penumbra:
Ok, he is right. Thanks for the explanation, The Bad Astronomer.
Oh, for Pete’s sake. Defraction pattern. . . wave length . . .Huygen’s principle.
You do not need to invoke wave-particle duality or anybody’s principle to get this. If you are standing on a plane with parallel lines, they appear to fan out from a point at infinity. Our perception of distance is good for things close to us; it is not so good for things at a great distance. If you look at people from a great height, they look small as ants. Those people are not really small, you know. It is because depth perception fails at great distances. The rays appear to fan out because of the scale of the distance.
I’ve seen the rays of the sun converge by looking at my shadow in muddy water. The rays look like my shadow is giving out rays of light – like some sort of halo.
Sorry I came to this discussion late, but I’ve been out sick. And Now Dr. Matrix and The Bad Astronomer have already given the right answer. I just need to add that, if you’re looking for documentary proof, look in my old stand-by, The Flying Circus of Physics by Jearl D. Walker. He has this question answered under the heading “The Rays of Buddha”. as usual, he gives references on the issue.
They are small and they fear me as i crush them between my thumb and forefinger.
Beatle, the trick is there is no explanation necessary, the sunbeams do not fan. They only appear to fan due to perspective as described so eloquently by others.
If you follow Phil (Bad Astronomer)'s links, you can get to this page which has a picture of the rays converging. Try explaining that with diffraction.
Oh, and Phil, I don’t get the joke. Is “crepuscular rays converging to the anti-solar apex” supposed to sound like some other phrase, like “transporting gulls across state lions for immoral porpoises”? I know the adage that if you have to explain it it stops being funny, so please forgive me for ruining your bit. 