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Fu-Kwun Hwang
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« on: January 29, 2004, 10:39:38 PM » |
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Registed user can get files related to this applet for offline access.If java program did not show up, please download and install latest Java RUN TIMEor A most charming example of chromatic dispersion is a rainbow.
When white sunlight is intercepted by a drop of water in the atmosphere, some of the light refracts into the drop, reflects from the drop's inner surface, and then refracts out of the drop.
As with the prism, the first refraction separates the sunlight into its component colors, and the second refraction increases the separation. The result is the rainbow.
This applet shows the physics of the rainbow. The black circle represents a drop of water in the atmosphere. Initially, red light is coming from the left; you can click inside the colored blocks to change the color of the incoming light. The incoming ray is unpolarized, which can be represented as a mixture of two polarized waves whose planes of polarization are perpendicular to each other. So the notation " 50%| 50%+" means that half is polarized in the up-down direction and half is perpendicular to the screen. Many things can happen to the light. - Part of the incoming ray is reflected back to the atmosphere (indicated by ray number 1). The intensity of each polarized component is shown along the ray path.
- Part of the light refracts into the drop, then refracts back to the atmosphere(ray number 2).
- Some reflects from the drop's inner surface, and refracts back to the atmosphere (ray number 3). This gives rise to the ordinary rainbow.
- Some reflects twice inside the drop, then refracts back to the atmosphere.(ray number 4) This gives rise to the secondary rainbow that is sometimes seen.
You can drag the incoming ray, move it up and down, and watch how the relative intensities change. R is the radius of the water drop; b is the vertical distance of the incoming ray from the center of the circle. The intensity of the light coming from rays 3 and 4 is plotted versus viewing angle. Click ^or vto change the scale. For ray number 3 there is a maximum scattering angle, and for ray number 4 there is a minimum -- this is why there are strong peaks in the scattered intensity. The rainbow is actually a disk of scattered light, but it is brightest at the edge; the disk for different wavelengths is a different size, and that is why we see the color effects there. You can click inside the white box, and see what will happen to white light. When light refracts, it follows the law of refraction ni sin(ctai)=nr sin( ctar) where n is the index of refraction. The number in the left-bottom corner i is the angle of incidence, r is the angle of refraction. Most of the light is refracted out by ray 2. When your eyes intercept the separated colors from raindrops, the red you see comes from drops angled slightly higher in the sky than does the blue. You see a circular arc of color, with red on the outside and blue on the inside. Click inside the colored box to show this effect. You can drop one of the rain drops,Try it! Did you notice that the rainbow consists of partially polarized light? Registed user can get files related to this applet for offline access.If java program did not show up, please download and install latest Java RUN TIMEor
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Fu-Kwun Hwang
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« Reply #1 on: January 29, 2004, 10:41:06 PM » |
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| name | direction of electric field | color |
| s-wave | perpendicular to the screen ( + ) | same color as the light |
| p-wave | in the up-down direction ( | ) | yellow |
This is an e-mail message from Neal Rasmussen (posted with his permission) I am a tornado chaser for 20 years. About 4 years ago I was driving through a McDonald's drive thru. As it was just after a pretty good storm, I had mys polarized yellow tinted flip-up sunglasses on. Low and behold I almost dropped my cigarette into my lap. There off in the east was a double rainbow! Not the kind I've seen dozens of times where the second one is reveresed and much outside the primary, but this was immediatly INSIDE the primary! Gaping with my mouth open and people behind me honking, I flipped my flip-ups up and the second inner one went away! I must have sat there for 2 minutes flipping my sunglasses. The colors were NOT reversed and it looked like one continuous double wide rainbow, with two complete sets of colors. I ruled out that the flip-ups where giving double vision as I looked at lights the next day, streetlights headlights, etc. and no doubles! Can this possibly be? Could a source of polarized light be at a different angle, perhaps the sun shining through a cirrus cloud or noctelucent (sp). Email message: Subject: circular rainbows Date: Fri, 4 Aug 2000 19:03:52 EDT From: Jrs3290@aol.comTo: hwang@phy03.phy.ntnu.edu.tw Hi, I am facinated by rainbows but am not smart enough to understand it all. I do know that the most amazing one I have ever seen was when I was in a small single engine aircraft above a layer of white clouds. The cloud cover was smooth and the sun made a shadow of my aircraft . As I looked at the shadow of the aircraft on the clouds I noticed it was encircled by a circular rainbow. The rainbow followed until the cloud cover changed and then disappeared. Sincerly, Jim Spencer My response: I was always dreaming to be able to see the same view as you have seen (whenever was on an airplane). What you have seen is a true rainbow. Circular rainbow can only be viewed from above the ground. When we were on the ground, at least half of them were missing. The viewing angle is about 42 degree. Subject: Re: circular rainbows Date: Sat, 5 Aug 2000 10:47:47 EDT From: Jrs3290@aol.comTo: hwang@phy03.phy.ntnu.edu.tw Hi, yes you may use the letter any way you like. If you do I wish you would let me know so I can look at it. The angle from where I was sitting in the aircraft and the shadow was about 45 degrees as I remember it and I wonder if the angle had been greater or less do you think I would still have seen a rainbow or was I just fortunate that day to be at the right place at the right time ?? Jim Spencer |
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« Reply #2 on: January 30, 2004, 08:09:50 AM » |
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Subject: I saw a Polarized Rainbow! Date: Sat, 14 Mar 1998 01:18:24 -0800 From: Neal Rasmussen < nealras1@airmail.net> To: hwang@phy03.phy.ntnu.edu.tw I am, as far as I know, the first to see a "Polarized Rainbow"! I think we should name this phenomona the "Rasmussen-Wang Rainbow". :-) I am a tornado chaser for 20 years. About 4 years ago I was driving through a McDonald's drive thru. As it was just after a pretty good storm, I had mys polarized yellow tinted flip-up sunglasses on. Low and behold I almost dropped my cigarette into my lap. There off in the east was a double rainbow! Not the kind I've seen dozens of times where the second one is reveresed and much outside the primary, but this was immediatly INSIDE the primary! Gaping with my mouth open and people behind me honking, I flipped my flip-ups up and the second inner one went away! I must have sat there for 2 minutes flipping my sunglasses. The colors were NOT reversed and it looked like one continuous double wide rainbow, with two complete sets of colors. I ruled out that the flip-ups where giving double vision as I looked at lights the next day, streetlights headlights, etc. and no doubles! Can this possibly be? Could a source of polarized light be at a different angle, perhaps the sun shining through a cirrus cloud or noctelucent (sp). Neal Rasmussen nealras1@airmail.net |
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« Reply #3 on: January 30, 2004, 04:38:12 PM » |
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From: NAPLES96@aol.comDate: Thu, 28 Oct 1999 08:58:38 EDT Subject: Interesting find! To: hwang@phy03.phy.ntnu.edu.twJust stumbled upon your observation while looking for reasons for a rainbow. Actually I had seen a "round" rainbow and was unable to find any comments on the subject. Have you any knowledge of one? I'm just an admirer of the beauty of the sky, here in Naples, FL. Thank you, |
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« Reply #4 on: January 30, 2004, 04:49:45 PM » |
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From: Ayuyroq@aol.comDate: Thu, 2 Dec 1999 16:48:07 EST Subject: (no subject) To: HWANG@phy03.phy.ntnu.edu.twMy youngest daughter did an elementary school science fair project on the effects of pollution on rainbows and she found the applet on how rainbows are formed, which is copyrighted by you, on line. Could you tell us how to credit this work done on line in her Bibliography? Thank you, A. |
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« Reply #5 on: February 22, 2004, 11:34:00 AM » |
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Great site with clear explanation. I thought the double rainbow that one sees emanates from light that enters very low on the raindrop and then reflected twice within the raindrop. Is that true? Your diagram seems to suggest that the primary and secondary rainbows are created by different paths of the same light and not seperate rays of light. Is there any way to add the perspective of the observer to your diagram to show the paths of the light producing what the observor sees (primary and secondary rainbows) and the angles at which the rainbows would be seen in nature. Is there anyway to also add the perspective of the observer to show why the color spectrum is seen as a "bow" or arc and why a rainbow would be seen as a circle from just the right perspective (e.g. airplane). Great site and thanks. Tom DeCoster Tadabq@aol.com |
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Fu-Kwun Hwang
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« Reply #6 on: February 22, 2004, 11:45:13 AM » |
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Registed user can get files related to this applet for offline access.If java program did not show up, please download and install latest Java RUN TIMEor from the following picture, you will find that the intensity of the first rainbow is about 2*4.5% of the incoming red light. So the intensity is indeed small. The rainbow you saw was coming from many different raindrop. The primary and the second rainbow also create from differnet raindrop and different light path. Remember light need to enter your eye for you to see the image. The angle shown on the applets is assume the sun light is horizontal. If the sun is higher you need to substract the angle of the sun ray relative to horizontal. If the angle is less than zero , you would not be able to see rainbow on the ground. That why you never saw rainbow at noon (after 9am or before 3pm) on the ground.  The angle for the second also shown on the applet, as indicated in the following picture.  The following applet show you why why the color spectrum is seen as a "bow" or arc. (The other half will be underground if there are raidrops and can refelect sun light, which is impossible.) However, it is possible when you were on an airplane. or
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Rainbow_Zanadar
Computer Engineer
Newbie
Posts: 1
Music, Computers, Rainbows.
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« Reply #7 on: February 22, 2004, 08:43:38 PM » |
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Nice explanations of the mathematics of rainbows.
A "Round" Rainbow will always be observed when the sun is directly behind you and the water droplets are directly in front of you and you are at an altitude that enables you to see the circle of light. I'm not entirely sure if the distance you are from the water droplets determines the size of the circle, I'll have to investigate more. The "circle" is a "Halo" effect similar to the effect you get on a foggy night when the moon is at its fullest.
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Le
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« Reply #8 on: October 10, 2005, 09:59:27 PM » |
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Hi!
Came across this site when researching light and the rainbow. Have found some really interesting information here. I dont actually work in or study science, but I am fascinated by it and always trying to inform myself in many scientific theories which I try to incorporate into my artwork(am in my final yr in art college, specializing in interdisciplinary studies). Anyway...
:oops: This will possibly be a stupid question but its something someone has recently told me about. I have been told that on one side of the rainbow there is a kind of blank space or void which is said to be unexplanable, romantically described as holding the mysteries of the universe, this fascinated me so much and am wondering if there is infact such a void?...
Thanks
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Fu-Kwun Hwang
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« Reply #9 on: February 25, 2006, 04:03:41 PM » |
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I receive the folllowing message from a user : Hi there, I took these shots, and more besides flying into Bristol on a commercial flight. The following are pictures attached with the email message  and  But I might say that the above two picture are not the same as the rainbow in the simulation. I also saw it once when I am in an airplane,too. I can not recall it's name, now. |
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gon
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« Reply #10 on: October 11, 2007, 03:39:38 PM » |
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Mr. Fu-Kwun Hwang, You are such a genius. My question is, how does double rainbow forms? I was once see a double rainbow when I am lying on the floor while fixing my jeep engine parts saturday morning. And I was amazed because usual rainbows are single. How do we know about it? My friends are also amazed with it. Thanks in advance. I have here an image of double rainbow: http://www.photocentric.net/gallery/rainbows/RPrainbow2.jpg-Ms. Gon. |
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Fu-Kwun Hwang
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« Reply #11 on: October 11, 2007, 09:00:19 PM » |
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I am not a genius. I learned it from standard textbook for physics. If you have enough resolution device, you even can see the third ranibow. But it will be very difficult, because the first two are pointing back to the direction of the sun, so you can see it while your back is face to the sun. (for the light coming from the sun, the intensity of the rainbow light will be too weak compared to the light from the sun, so you would not be able to see it).
Intensity for the second rainbow is even weaker(2%) than the first one (about 5% of the intensity of sun light).
So normally, you might not notice it.
If you drag the horizontal red line with your mouse from the top and move it downward slowly.
Check out the angle for #3 ray (at the bottom you will find 3):
you will find the angle increase first, then at about 42 degree it become smaller again as you continue to drag the line down.
And the maximum angle is the angle you will find rainbow for red light (when the ray of incoming sun light is horizontal).
You will find #4 ray at the top. But when you drag the red line lower than the center of the water drop(big white circle)
the # 4 ray starts to point download. when it reach near 50 degree(also the maximum angle), that is the angle you will find the second rainbow.
Normally, when you watch the rainbow, the ray of the sun light is not horizontal.
If it is 15 degree higher, you need to substrate the 15 from 42 (or 50). So when the sun is too high, there is no way you will find rainbow in the ground (you might see rainbow from high enough mountain).
So you might be able to see the rainbow in the early morning or late in the afternoon.
I hope the above information will help. I upload the picture for the rainbow, so more user can see the beautiful rainbow.
And I hope many of you can enjoy the fun of physics as I do.
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« Last Edit: October 11, 2007, 09:05:06 PM by Fu-Kwun Hwang »
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gon
Newbie
Posts: 5
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« Reply #12 on: October 12, 2007, 07:10:15 AM » |
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Wow... That was the double rainbow photo I have given you. It was really great to see. I can't really imagine that there is still a third rainbow.  Wow ...... Thanks a lot. I gonna tell this to my friends and also ofcourse to meet you Mr. Fu-Kwun Hwang. We are going download movie about rainbows! |
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« Last Edit: October 23, 2007, 08:51:09 AM by gon »
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nonymou
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« Reply #13 on: May 13, 2008, 11:33:16 PM » |
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Dear Fu-Kwun,
Thank you for sharing this excellent work you have done. This is a tremendous resource for understanding physics! I am not a physicist, but I am working on a solar energy project and need to understand something about optics for concentrating sunlight with a lens, including the prismatic effect, as demonstrated by your rainbow applet. I hope to be able to create an applet of the project I'm working on, building on the 'thick lens' and the 'rainbow'. If I am successful, I'll post it for others to see.
Thanks again.
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Fu-Kwun Hwang
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« Reply #14 on: May 13, 2008, 11:38:52 PM » |
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Good! I hope to be able to see your work soon. Good Luck!
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candacedwan
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« Reply #15 on: May 25, 2008, 12:24:11 PM » |
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The effect of brightness inside the rainbow and darkness outside the rainbow intrigues me. Can you help me to understand this? Does the rainbow behave as a giant lens?
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Fu-Kwun Hwang
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« Reply #16 on: May 25, 2008, 11:55:30 PM » |
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Did you noticed that there is a intensity vs angle diagram in the simulation?
Check out the diagram and think how it is related to your question.
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Nick Lu
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« Reply #17 on: June 01, 2008, 01:30:02 AM » |
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Dear Admin. Fu-Kwun Hwang
I've already read your article about the rainbow, and I love it pretty much!! However, I still don't quite understand why the rainbow always looks like an arch as raindrops are everywhere, why do I only receive the refraction light spectrum from that arch not anywhere else? Besides, I've no idea how the hell this happened in these pictures as I tried to think about it but just had no idea... and in picture 721e67.jpg, the color of the cloud between the two rainbows is darker than the outside part, odes it have something to do with this phenomenon?
Thank you very much!
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Fu-Kwun Hwang
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« Reply #18 on: June 01, 2008, 11:51:20 AM » |
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Registed user can get files related to this applet for offline access.If java program did not show up, please download and install latest Java RUN TIMEWe can drag the sun ray up and down and we will find ray #3 can be any angle. If all the intensity of ray #3 are all equal, we would not be able to see rainbow. But the intensity of ray #3 has a maximum value at particular angle (for red light near 42 degree). The diagram in the simulation shows intensity of ray #3 and #4(secondary/outer and weaker rainbow) as function of angle. There is a gap in which no ray will be refracted, so there is a region which will be darker in the space. If we accept for horizontal sun ray, the view angle for red light will be near 42 degree (different angle for different color sun ray) The light might enter our eye for us to see it. So all the light enter our eye with 42 degree is a cone. If you move to a different position, you are viewing another rainbow. So the rainbow saw by different people are coming from sun ray refracted from different rain drop. (Your rainbow is for your eyes only!) But 42 degree is for horizontal sun ray. If the sun is located at higher angle, then the angle you will find rainbow will be smaller. We will not be able to find rainbow at ground if the sun is above 42 degree (for example: at noon). So we only find rainbow in the early morning or before sun set. I hope the above explanation can help you understand more about rainbow.
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Fu-Kwun Hwang
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« Reply #19 on: June 26, 2008, 10:47:31 AM » |
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Dear Fu-Kwun Hwang,
I was looking for some good explanation about rainbow physics when I found this problem and still i cannot figure out an answer to this. I've been studying some optics this year and I've been told that the primary rainbow has always the red colour on its external part. Now, as seen in picture "Rainbow1.png" the red ray is refracted downward; so the observer should perceive it as the lowest one. Could you please give me the answer to this?
Different color of sun light refracted from the same water drop are refracted at slightly different angle. The distance between the person who saw the rainbow and the water drop are normally very large. So different color light refracted from the same water drop would not enter the same person's eye. The red light and the blue light saw by the same person are sun light refracted from different water drop. Please check out rainbowcolor.jpg If you move to different position, the rainbow you saw was not the same one. And different person will see rainbow refracted from different water drops. Everyone saw his own rainbow. The rainbow you saw is for your eyes only. |
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