Underwater Light: Newsletter Challenge (12/02/08)

Have you stopped beating your wife?

Does it remain unchanged? Who said it was unchanged... so that it could remain so?

I cannot think of any real-world condition under which the light would not change in several ways as it goes through the water and air and water/air interfaces.

Don't forget the light reflected as the beam inside the bubble encounters the air/water boundry on the way out. This will be a loss in The reflected light will end up exiting the bubble in every direction.

You are right about the reflections. I don't have time to do the calculations, but in my work I do look at a lot of back-lit bubbles, and generally speaking it appears that a lot of the incoming light does get through. Generally the bubbles look darker towards the edges, where the low incidence angles of the light leads to higher reflectivity, but the centers are fairly bright. This is of course very subjective, but I would guess that maybe 2/3 of the incident light is refracted, maybe 1/3 reflected. The bubble therefore works more as a negative lens than as a mirror.

You have the full, correct answer. A bubble of air in water is NOT(bubble of water in air). Since a bubble of water in air causes convergence (bi-convex), a NOT(bubble of water in air) causes divergence. Sorry-just couldn't resist making Boolean bubbles.

All bubbles must be spherical, then

Yes. But in my and Don Ho's world, all bubbles are perfect.

Perfectly spherical bubbles so tiny they behave as Rayleigh scatterers?

You don't suppose that's how Moses turned the Nile red...? Miriam was under there with an air stone.

confounded minimal tension.....

I'm too lazy to make a dodecahedron.

This is the best answer here. Keep it simple. The fact that we can see the bubble from any vantage point. and aim a flash light at it, indicates without debate the light is reflected from every surface, inside and out, in every direction.

Also, the light is changing constantly before it gets to the bubble and after it exits the bubble because it is reflecting from water molecules. You will see the beam from the flashlight because of this.

Several options are open as already commented by other colleagues.

One more: What type of light, white? monochromatic?

If white light go through the interface of two media with different refraction index in a different direction but normal, refracted beam is not an homogeneous white light one, but a separation of all visible spectrum wavelengths in the form of a rainbow (have you see rainbow, or the simple school experiment of a white light beam and a prism?)

If the light is monochromatic, no rainbow like separation occurs, just the effect predicted by Snell's law. If the incident angle is different from 0º, the emerging beam should be parallel to the incident because two consecutive and inverse refractions. And don't forget that in this case, if the incident angle is 0º (beam normal to surface, in this case going through the bubble following a bubble diameter) no refraction will occur, just transmission.

Note: I'm assuming that bubble is spheric. If it has an icosahedron form the results surely will be different.

Viewing the problem from other point, any light beam going through water gets dispersed and attenuated as you can see? if you dive a little bit.

Kind regards

"...What type of light, white? monochromatic?"

White. The OP said the light was coming from a flashlight.

"Note: I'm assuming that bubble is spheric. If it has an icosahedron form the results surely will be different."

They only look like icosahedrons when you drink large quantities of German beer from a Klein bottle:

Hi europium

White. The OP said the light was coming from a flashlight.´

The OP says "could be" a flashlight. He doesn't assure it. And it doesn't makes any objection to the fact that the flashlight can have a filter/polarizer....

I assumed spherical bubble to simplify (icosahedron was a joke)

We can consider the geometric form of bubble undetermined, so the incident angle may be the same as the out coming angle (parallel lines anyway) if the curvature is the same just in the case of spherical or symmetrical bubble. In any other case it's different, Snell Law will give us the answer

Obviously most colleagues seems agree the beam changes somehow.

I never saw a bubble like a icosahedron even I've drunk a lot of German beers (Alt, Kölsh, Lager, Hefe Weiss, etc) and as much British (Ale is my favourite) but I prefer a 18 years old Macallan (my incomes doesn't allows me drink 50 years old one)

And you'll be a bit faster and reply a post in less than a week

Kind regards

I've no idea if this (air bubble in water) helps or not;

Great effort there Mark. GA

Scroll 2/3 of the way down here - I can't blow decent smoke rings, never mind underwater bubble rings ;

http://www.oceanlight.com/log/2008/06/

I will have to say it depends on factors such as the density of the water, particle obstruction (because there is no guarantee the bubble will remain intact through out its period underwater), the speed the bubble travels, how big the bubble is (this affects the # of collision rates of the light particles on the bubble surface walls) ,the refractive index and the direction of the light.

If all these factors are taken care of and ignored, the light will remain unchanged itself.

Here's a simplified sketch of a plane-wave beam striking the bubble on-center. (Not exactly to scale, but approximately so.) The beam crosses from left to right. As it traverses the bubble it expands due to the air bubble index of refraction being 1.00 whereas the water has an index of refraction of 1.33, and due to the curved surface of the bubble where the beam first makes contact. Snell surface losses are ignored.

An improved drawing (slightly better to scale) with some more info added:

Hi, Kinsale!

Where is the scattering from internal wall reflection?

Mark

Geez, I'm not running Zemax or Code V. I'm just looking at the most basic refraction/TIR effects and running a few calculations with a hand calculator. Just trying to keep it simple, so as I said in my earlier response I was ignoring the Snell surface losses (which of course are the surface reflections.)

By the way, if you want to see what the effect would be with a lot of bubbles go pour yourself a glass of Guinness. Yet another reason for drinking Guinness -- it's science!

I'm with you on the Guinness Kinsale...

No , the light will be reflected in various directions. wv pipefitter

If one looks through the bubble directly to flash-light he would see dark ring occuring due to total internal reflection of water/ air boundary and in central zone of bubble extremely demagnified view of flash-light (focal length of negative lens formed by bubble equal to -R, where R is radius of the bubble).These speculations lets to conclude that direction of light would change drastically - one could see dark spot with shining center.

Concerning attenuation - brigtness would be attenuated nearly 2.5 times mainly due to total internal reflection

Yes, the light would have to WANT to change, but considering that it chose it's course of shining through the bubble, it must have wanted to.

Other than inquiring about WHY the light chose to shine through an underwater bubble and not cross a road, there are too many variables to think it could possibly remain the same.

Given the various shapes of an underwater bubble, it would depend on which angle the beam pierced the bubble - the angle of incidence would be different in each case, so the angle of refraction would correspond to each change in beam angle.

A study should be made of this, preferably in clear, warm waters - my recommendation would be the waters of the Grenadines, or Belize, although a solid case could be made for Antigua. Being experienced at blowing bubble rings at depths to 100' I should be "deeply" involved in this project.

On re-reading the challenge, I realize the question is "when the light emerges from the bubble, does it remain unchanged?"

This is clearly a trick question, since whether the light remains unchanged after emerging from the bubble depends entirely upon what else we do with it. And by using the word "remain", the poser of the question indicates that this light is not expected to change during initial bubble transit. It opens up a new field of conjecture, detailing the fate of the light post-bubble.

e.g. We could have another bubble waiting and check the nature of any changes in the light as it interacted with the new bubble.

We could thrash the water briskly to set up currents that might each bend the emerging light depending upon their angle of incidence to it.

We could just leave it completely alone, in which case the answer would be that it would remain unchanged.

We could pass it through filters or prisms or place mirrors in its path to make it take on new directions and break down into its component parts.

The energy of the light would probably not change, since water is just another medium for light conductivity.

Mark

I guess it boils down to "What constitutes change in this context?" Does the light changing direction constitute change? Certainly in this sense the light is not unaffected on passing through the bubble! The ambiguity of the word makes plausible a number of alternative interpretations. And since no other info was given (and since none of us here seem to be telepaths) we really don't know what, exactly, does the author mean by 'change.' The question remains ambiguous.

Example:

"Hey Buddy, can you spare a dime?"

"Spare it from what?"

Hi, europium!

And, since we have little to no information about the initial bubble, other than the statement that the light is unchanged after passing through it, we must assume an initial bubble of a character that does not change light. Suspend disbelief, as it were, in order to get at the heart of the matter...which is: "what happens next?"

Suppose, for example, there were to be no initial bubble. What would happen to the light as it flashed through the bubble-less water? Given that the initial bubble did not, according to the question, alter the light passing through it in any way, would there be any difference as to whether the initial bubble existed or didn't?

In the context of post-bubble, any change constitutes "change". Perhaps we should take post-bubble as the intial entry point of the light beam into water and examine what occurs upon initial entry (magnification due to bending) in calculating our response.

Mark

Further to this conceptualization of the challenge's intent, there is air in the bubble. Taking that air as a starting point (as though the light source was located in the bubble and shining from there into the water), and the entry of the beam from that bubble-contained air through the bubble's theoretically non-interfering surface, the shaft of light will bend as it passes through the water, unless it originates at a point directly perpendicular to the water's surface.

So the answer is yes, unless the light source is directly perpendicular to the surface of the water outside the bubble, the light will "change" due to the larger refractive index of the more dense medium.

Mark

Some of the light will be trapped in the bubble forever and ever and ever. It has to go in at the right angle, but that's not my problem. I'm just being a bit of a plank to keep this puppy running. Bubbles have a dark rim, and spots on the poles (but you can't move fast enogh to check it). The dark bits are the trapped light.

It seems obvious to me without too much analysis, that if the light did NOT change then the bubble would be totally invisible assuming backlight (from the POV of the viewer) is the only light source. Since, in my experience, I have seen bubbles intervene between me and a light source, I would say the light does change to some extent.

My point is, I'll get out the calculators and software when needed but on a 'yes or no' question with a common sense answer, I defer to experience.

Hello europium,

I think your statement should be:Those who think bubbles don't change light sight have obviously never tasted (enough) beer

Assuming the water to be pure (without particles) the entry will refract the light by a certain angle (based on coeff of refraction). The exit will them refract the ray by the same angle in the opposite direction. Thus the ray will emerge unchanged in direction.

"Thus the ray will emerge unchanged in direction"

The question simply asks will the ray change. Direction is not the only change possible is it? Not meant to pick on you, it does not seem that any other aspect of the ray has been considered, Any thoughts?

That is entirely incorrect. As the argument would work equally well for a crystal ball or even an ordinary symmetrical lens you could try looking what happens with one of those to see where you went wrong.

explanation seems to be in order. no change.

Presumably you base this thought on the fact that the curvature of the bubble surface at the second edge is reversed, and* that if the change in the refractive index was the same the ray would return to its original direction. But, in fact the change in refractive index is reversed - on entering the bubble the index decreases, on leaving the bubble the index reduces. That means that the refractive change in direction at the second surface of a spherical bubble would add to the original. Then of course there are surface reflections.

But, as stated by others, the very fact that you are able to see bubbles in water should be enough to make you question any supposed logic that suggests the bubble does not affect the light.

*neglecting the change in position within the bubble

We only think we know what is happening because when we look at the bubble, we see a bubble instead of the flashlight that sent the light in the first place. When we look at something that is red, we say it is red. The light contained by the object is every part of the spectrum except red. What we see is all that is reflected. So when we define an object as red, we are actually defining it as all colors that it isn't. So when we say that we see a bubble, we are seeing everything that it isn't. So I say that all we ever know is everything except what is really there. The only reason we say a bubble is there is because the light does not pass through it unchanged. The light that strikes our eye is all of the light that is rejected by the object. We think this one is a bubble..

on entering the bubble the index decreases, on leaving the bubble the index reduces

So the index is increasingly lowering as a whole. I know how it feels, I can't get back on track either .

Kris is right - I'm guilty (yet again) of a garbling: it should of course have read: on entering the bubble the index decreases, on leaving the bubble the indexes increases.

It's impossible to underestimate my contribution here.

No. Because the bubble is under tension (as a result of being pushed to the surface by the weight of the water), it will not have a perfectly spherical shape therefore the angle of incidence of the light beam will not equal the angle of exit of the light beam with respect to the plane of the flashlight which is perpendicular to the beam of the flashlight. In addition the beam of light, at the exit point, will be diminished slightly due to internal reflections at the point where the water meets the bubble.

No, it should be the same beam but it will be inverted.

Come to think of it, I've never seen an upside-down bubble...