Explanation: What lies at the end of a rainbow? Something different for everyone. For the photographer taking this picture, for example, one end of the rainbow ended at a tree. Others nearby, though, would likely see the rainbow end somewhere else. The reason is because a rainbow's position depends on the observer. The center of a rainbow always appears in the direction opposite the Sun, but that direction lines up differently on the horizon from different locations. This rainbow's arc indicates that its center is about 40 degrees to the left and slightly below the horizon, while the Sun is well behind the camera and just above the horizon. Reflections and refractions of sunlight from raindrops in a distant storm in the direction of the rainbow are what causes the colorful bands of light. This single exposure image was captured in early January near Knight's Ferry, California, USA.
APOD Robot wrote:
What lies at the end of a rainbow? Something different for everyone. For the photographer taking this picture, for example, one end of the rainbow ended at a tree. Others nearby, though, would likely see the rainbow end somewhere else. The reason is because a rainbow's position depends on the observer.
Who knew there were so many pots of gold at the subjective ends of different people's rainbows?
(Oh, and by the way, wouldn't it be fun to see the rainbow "sideways" - as it is seen in the landscape/pot of gold illustration above - so that it really looked like a solid physical object like a bridge? Though I guess that if we did see the rainbow like that, it would be time to panic, no matter what the Hitch-Hiker's Guide to the Galaxy tells us?)
Why is the rainbow’s spectral dispersion (i.e., width) larger near the horizon?
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Mon Mar 13, 2023 4:33 pm
by Chris Peterson
Don M wrote: ↑Mon Mar 13, 2023 3:40 pm
Why is the rainbow’s spectral dispersion (i.e., width) larger near the horizon?
I'd guess we're just seeing lens aberration and mapping issues. Typically the pixel scale is larger around the edges of a field than at the center, which makes things look somewhat compressed as you near edges.
Don M wrote: ↑Mon Mar 13, 2023 3:40 pm
Why is the rainbow’s spectral dispersion (i.e., width) larger near the horizon?
I'd guess we're just seeing lens aberration and mapping issues. Typically the pixel scale is larger around the edges of a field than at the center, which makes things look somewhat compressed as you near edges.
Pixel scale? You can't mean the size of the pixels in a CCD detector, since those are surely uniform throughout, right? Does your statement apply to both film and CCD images? Is it a "feature" of lenses? (yeah, I still suck at optics...) ...Oh, maybe a lens always spreads light out at the edges so that whatever is detecting it - film or CCD - will detect a smaller area of the actual thing being imaged?
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Mon Mar 13, 2023 7:41 pm
by johnnydeep
Tree to mothership: "Beam me up, Scotty"!
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Mon Mar 13, 2023 9:06 pm
by orin stepanek
The rainbow tree; the rainbow tree! The gold is under the rainbow
tree! & If you drink some Irish whisky you'll feel really good!
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Mon Mar 13, 2023 9:24 pm
by eljayhalflife
I drove through a rainbow once, but no one believes me. I was on I-5 in Redding, CA crossing a highway bridge over the Sacramento River, very low to the water. I was on the phone to my niece and was flabbergasted that the colors actually beamed across my arms and the passenger seat as I went through. I saw the rainbow, of course, but I always thought it impossible to go through one. And before you ask, I was on my way home from working all day as a nuclear medicine technologist, so I wasn't under the influence of anything but fatigue.
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Mon Mar 13, 2023 10:32 pm
by orin stepanek
eljayhalflife wrote: ↑Mon Mar 13, 2023 9:24 pm
I drove through a rainbow once, but no one believes me. I was on I-5 in Redding, CA crossing a highway bridge over the Sacramento River, very low to the water. I was on the phone to my niece and was flabbergasted that the colors actually beamed across my arms and the passenger seat as I went through. I saw the rainbow, of course, but I always thought it impossible to go through one. And before you ask, I was on my way home from working all day as a nuclear medicine technologist, so I wasn't under the influence of anything but fatigue.
Don M wrote: ↑Mon Mar 13, 2023 3:40 pm
Why is the rainbow’s spectral dispersion (i.e., width) larger near the horizon?
I'd guess we're just seeing lens aberration and mapping issues. Typically the pixel scale is larger around the edges of a field than at the center, which makes things look somewhat compressed as you near edges.
Pixel scale? You can't mean the size of the pixels in a CCD detector, since those are surely uniform throughout, right? Does your statement apply to both film and CCD images? Is it a "feature" of lenses? (yeah, I still suck at optics...) ...Oh, maybe a lens always spreads light out at the edges so that whatever is detecting it - film or CCD - will detect a smaller area of the actual thing being imaged?
Pixel scale refers to the angle subtended by a pixel (or between the centers of two adjacent pixels). It isn't the same across an entire image. One reason is because of geometric aberration in the lens system, and another is because you are mapping a spherical world onto a flat image. This is visually extreme in fisheye images (which this isn't, of course, so the effect is more subtle).
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Tue Mar 14, 2023 1:55 am
by hypermetabolic
And what is that fainter rainbow just inside the main one, most visible near the horizon?
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Tue Mar 14, 2023 6:49 am
by Ann
hypermetabolic wrote: ↑Tue Mar 14, 2023 1:55 am
And what is that fainter rainbow just inside the main one, most visible near the horizon?
That's a supernumerary rainbow. There can be lots of them.
I'd guess we're just seeing lens aberration and mapping issues. Typically the pixel scale is larger around the edges of a field than at the center, which makes things look somewhat compressed as you near edges.
Pixel scale? You can't mean the size of the pixels in a CCD detector, since those are surely uniform throughout, right? Does your statement apply to both film and CCD images? Is it a "feature" of lenses? (yeah, I still suck at optics...) ...Oh, maybe a lens always spreads light out at the edges so that whatever is detecting it - film or CCD - will detect a smaller area of the actual thing being imaged?
Pixel scale refers to the angle subtended by a pixel (or between the centers of two adjacent pixels). It isn't the same across an entire image. One reason is because of geometric aberration in the lens system, and another is because you are mapping a spherical world onto a flat image. This is visually extreme in fisheye images (which this isn't, of course, so the effect is more subtle).
So, I guess you mean something like the effect that I try to show in this image of red rays of light from a lens hitting a blue detector, where the same angle covers more of the detector the further off center it is?
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Tue Mar 14, 2023 4:34 pm
by Don M
Basically, optical “distortion.” Wish we could see the full image to be sure.
Pixel scale? You can't mean the size of the pixels in a CCD detector, since those are surely uniform throughout, right? Does your statement apply to both film and CCD images? Is it a "feature" of lenses? (yeah, I still suck at optics...) ...Oh, maybe a lens always spreads light out at the edges so that whatever is detecting it - film or CCD - will detect a smaller area of the actual thing being imaged?
Pixel scale refers to the angle subtended by a pixel (or between the centers of two adjacent pixels). It isn't the same across an entire image. One reason is because of geometric aberration in the lens system, and another is because you are mapping a spherical world onto a flat image. This is visually extreme in fisheye images (which this isn't, of course, so the effect is more subtle).
So, I guess you mean something like the effect that I try to show in this image of red rays of light from a lens hitting a blue detector, where the same angle covers more of the detector the further off center it is?
pixel scale.png
That's a form of tangent error, a simple consequence of geometrical optics. But no lens system can uniformly map its spherical input to a planar output without some kind of distortion. That's a kind of mapping error.
Chris Peterson wrote: ↑Mon Mar 13, 2023 10:35 pm
Pixel scale refers to the angle subtended by a pixel (or between the centers of two adjacent pixels). It isn't the same across an entire image. One reason is because of geometric aberration in the lens system, and another is because you are mapping a spherical world onto a flat image. This is visually extreme in fisheye images (which this isn't, of course, so the effect is more subtle).
So, I guess you mean something like the effect that I try to show in this image of red rays of light from a lens hitting a blue detector, where the same angle covers more of the detector the further off center it is?
pixel scale.png
That's a form of tangent error, a simple consequence of geometrical optics. But no lens system can uniformly map its spherical input to a planar output without some kind of distortion. That's a kind of mapping error.
Ok, so what I tried to depict is not "pixel scaling"?
So, I guess you mean something like the effect that I try to show in this image of red rays of light from a lens hitting a blue detector, where the same angle covers more of the detector the further off center it is?
pixel scale.png
That's a form of tangent error, a simple consequence of geometrical optics. But no lens system can uniformly map its spherical input to a planar output without some kind of distortion. That's a kind of mapping error.
Ok, so what I tried to depict is not "pixel scaling"?
"Pixel scale" just refers to what I said: the angle subtended by a pair of adjacent pixels. It is not uniform across any image for a variety of reasons, including the one you depicted.
Chris Peterson wrote: ↑Tue Mar 14, 2023 4:40 pm
That's a form of tangent error, a simple consequence of geometrical optics. But no lens system can uniformly map its spherical input to a planar output without some kind of distortion. That's a kind of mapping error.
Ok, so what I tried to depict is not "pixel scaling"?
"Pixel scale" just refers to what I said: the angle subtended by a pair of adjacent pixels. It is not uniform across any image for a variety of reasons, including the one you depicted.
Ok, thanks.
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Tue Mar 14, 2023 7:23 pm
by Fred the Cat
How to get useful work out of a rainbow. No pot of gold but fun.
Re: APOD: Rainbow Tree (2023 Mar 13)
Posted: Tue Mar 14, 2023 8:13 pm
by johnnydeep
Fred the Cat wrote: ↑Tue Mar 14, 2023 7:23 pm
How to get useful work out of a rainbow. No pot of gold but fun.
Future meteorologist or astrophysicist in the making perhaps. I notice the dad said "when the water hits the sunlight", as opposed to "when the sunlight hits the water", but I guess it doesn't make much of a difference, though both are necessary in this case
Fred the Cat wrote: ↑Tue Mar 14, 2023 7:23 pm
How to get useful work out of a rainbow. No pot of gold but fun. :ssmile:
Future meteorologist or astrophysicist in the making perhaps. I notice the dad said "when the water hits the sunlight", as opposed to "when the sunlight hits the water", but I guess it doesn't make much of a difference, though both are necessary in this case
And then there's this. No future meteorologists or astrophysicists in this family!
_
Fred the Cat wrote: ↑Tue Mar 14, 2023 7:23 pm
How to get useful work out of a rainbow. No pot of gold but fun.
Future meteorologist or astrophysicist in the making perhaps. I notice the dad said "when the water hits the sunlight", as opposed to "when the sunlight hits the water", but I guess it doesn't make much of a difference, though both are necessary in this case
And then there's this. No future meteorologists or astrophysicists in this family!
_
Click to play embedded YouTube video.
Pretty sad. But it also makes ME ask just what's in the water down there to cause such benightedness. And if she had half a brain, she'd realize that she can produce her own pots of gold this way on demand and become rich! Which brings to mind a movie I liked that had a similar "do something (bad) and get rich" theme - https://en.wikipedia.org/wiki/The_Brass_Teapot. I won't spoil the plot, but it's thought provoking.
Rainbow Tree
& If you drink some Irish whisky you'll feel really good! 
