# How broad is the rainbow spectrum?

1. May 4, 2005

### Phobos

Staff Emeritus
We see red to violet but how much further does it actually extend? I suppose it comes down to (1) the wavelengths of light not strongly absorbed by the atmosphere and (2) the limits on a water drop sufficiently refracting the longer/shorter wavelengths. Is the invisible portion of a rainbow simply limited to the near infrared/ultraviolet?

2. May 4, 2005

### The Bob

Light is a part of the electromagnetic spectrum. The spectrum (starting from the longest wavelengths) goes: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-radiation and gamma rays. I assume there are some more on either side but I do not know of them. The wavelengths go from kilometers to nanometers.

Visible light is the only radiation that can be seen (hence the name). All of the frequencies of this portion are not absorbed by the stratosphere (well... enough can get through for us to see in all the colours of the rainbow). The visible region is limited between infrared and ultraviolet.

Also try looking at light through a defraction grating. It will show you all the colours that visible light produces.

Hope that helps a little.

3. May 4, 2005

### chroot

Staff Emeritus
The Bob,

I don't believe Phobos was looking for an explanation of the electromagnetic spectrum (though you did a superb job) -- I believe he was asking about the specifics of water droplets suspended in air. We all know that water droplets can refract visible light (that's a rainbow), but can they also refract radio waves? What about x-rays?

This, I don't know either. The size of the droplets is probably the most important factor. (Consult hyperphysics for some illustrations of light paths in water droplets: http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/rbowpath.html) You'd need rather large drops of water to appreciably refract microwaves (radar, anyone?), and you'd need unbelievably tiny droplets to appreciably refract x-rays; such droplets have such a large surface-area to volume ratio that they probably aren't stable in air -- they'd evaporate immediately.

- Warren

4. May 4, 2005

### Phobos

Staff Emeritus
chroot - yep, that's what I meant (but thanks, The Bob!)

Your assessment makes sense. Probably safe to rule out xrays or smaller and microwaves or larger. So I'd be curious to find out how far into the UV/IR it can go. I didn't see anything from a quick Google search....although it seems that IR was first discovered by the same curiosity of looking just beyond the visible spectrum
http://coolcosmos.ipac.caltech.edu/cosmic_classroom/ir_tutorial/discovery.html :)

5. May 4, 2005

### chroot

Staff Emeritus
Yes, but Herschel discovered IR with a prism, not a water droplet.

- Warren

6. May 4, 2005

### krab

There is a really nice graph of the absorption spectrum of water in Jackson (Classical Electrodynamics, Fig. 7.9, p. 291 in 2nd edition). It shows that water is transparent only for a very narrow frequency range that coincides with our visible light. If you think about it, it makes sense that this is not an accident. It is already as opaque at 20,000 Angstroms as it as at microwave frequencies. Anyway, that means that the rainbow does not extend very far beyond visible.

7. May 5, 2005

### The Bob

Oh..... *feeling embarrassed*..... I see. I do apologise Phobos. I didn't get the point. I didn't think you would have a problem with the electromagnetic spectrum but for some reason I thought that was what you were asking. Really quite sorry.

8. May 5, 2005

### Chi Meson

This seems like a question for ZapperZ. Can anyone get his attention?

9. May 6, 2005

### ZapperZ

Staff Emeritus
Ok.. Phobos got my attention...

Not sure if I can add anymore. Krab has give a sufficient explanation for it. I do know the UV part of the spectrum is highly absorbed by something as simple as a piece of clear ordinary glass, and those cheap plastic goggles that students use in labs (and I don't mean computer labs either! <looks at neurocomp>). So it would make sense that the UV end would not get very far through a water droplet.

The IR part, I am not sure.....

Told ya I can't add too much to this... :)

Zz.

10. May 6, 2005

### Integral

Staff Emeritus
This link has a chart showing the entire solar spectrum. I cannot help but notice that the peak of the solar spectrum corresponds with the center of what we call the visible spectrum or most of what we see in a rainbow. Coincidence, I doubt it, intelligent design... LOL.
life forms learning to use an abundant energy source.. most likely.

11. May 7, 2005

### Nereid

Staff Emeritus
This seems like a pretty cool site, lots of data, original sources, etc on the absorption spectrum of water.

So little to add here, except perhaps fill in some details etc:
- if there's no EM going into the raindrops, there will be no spectrum (duh!); this means (for example) that there will be no UV shortward of ozone absorption cutoff, irrespective of how transparent water is to those wavelengths
- the range of sizes (and shape) of the raindrops matters, esp wrt the intensity of the rainbows (plural)

12. May 7, 2005

### dextercioby

One of my teachers at my hometown university wrote a book called "The Rainbow".I didn't read it,yet light diffusion really got me interested once and bumped into this website

http://www.philiplaven.com/index1.html

Daniel.

13. May 7, 2005

### dextercioby

14. May 7, 2005

### Gokul43201

Staff Emeritus
First thing that came to mind when I saw this thread was the section in Jackson (that Krab mentioned). For those that have the third edition, it's in Ch. 7, Sec 7.5 E, pg 314. There appears to be a little room on the high frequency side (in the very near UV). For instance,
$$\alpha _{700~nm} = \alpha _{200~nm)$$.

Don't know what's wrong with LaTeX....the absorption coefficients are equal at 200 and 700 nm.

Last edited: May 7, 2005