It's a good thing this never came up on a test

May 25, 2010 5:27 PM

I think I heard a lie from a cave tour guide as a kid, and it's only recently that I realized I took it for granted as a property of optics. Can you confirm this?

When I was a kid, I got to go on a couple of cave tours, the well-lit, hour-long, perfectly safe kind. I think this particular one was in Arkansas.

There was a wooden footbridge that we crossed over a pool of perfectly still, clear water. The bottom was covered with smooth stones, and it looked about two feet deep. It was lovely; I think I may have stopped to reach into the water. The tour guide asked us to guess how deep we thought the water was. It might look just a few feet deep, he said, but that was only because this water was so perfectly pure and still that it looked clearer than any other water, and appeared very shallow. The water was actually sixty feet deep, he said, so be careful! Naturally I clung to my dad after that.

It only occurred to me the other day that I had still believed him all this time. That's the perfect lie to tell to get a kid to behave and stay on a footbridge! I've done a lot of swimming and scuba diving since, and I just assumed that, since all water is impure in comparison to an underground cave pool, there was never any reason for me to see that illusion again. Now that I consider it, I feel like Karl Pilkington for not having questioned it. My seventh-grade science understanding of refraction isn't helping me, but, like all of us, I do know that a perfectly clear piece of glass can, under the right circumstances, make something look closer.

So, in sum, is it ever true that water with a lack of particulate matter will present the illusion, from above, that the water is much shallower than it is?

posted by Countess Elena to science & nature (19 answers total)

It seems logical. In the absence of obvious visual cues (trees getting smaller farther away), we sort of estimate distance based on the visual degradation of objects in the field of view - close objects are sharp and far objects are fuzzy.
Water is a natural lens, so I can see how very clear water could give you a sharp/close impression of things that are further away than the same image would represent in the air.
posted by L'Estrange Fruit at 5:45 PM on May 25, 2010

I don't know about a few feet vs sixty feet, but water does have a higher index of refraction than air, which causes things to look closer. The Wikipedia article on refraction discusses this half way down the explanation section. You can also easily see it for yourself; just take a glass of water, stick a straw into it at an angle, look from above, and observe how it appears to bend. Alternately, stick a ruler in, and observe the perceived distortion in size.
posted by JiBB at 5:46 PM on May 25, 2010

Refraction will definitely make things under water appear closer than they really are, and I guess the lack of depth cue from hazy water will increase this impression. However, 2 ft versus 60ft sounds like a bit of a stretch...
posted by Jimbob at 5:48 PM on May 25, 2010

Water has a higher index of refraction than air. What this means in simple terms, is that light has a harder time traveling through water, so it goes slower. When you shine light at an angle to the surface of a pond (or glass or something like it), the light will bend towards the surface. This is called 'Snell's law'

What this means in your case is that the pool will look shallower, no matter what kind of water is in it.

But, normally, your 60ft deep pool would look about 40ft deep. I don't know why you'd guess it to be 2ft or so... maybe the particulate matter just gives you a sense of scale.
posted by chicago2penn at 5:58 PM on May 25, 2010

Nemo33 is the deepest diving pool in the world evidently. 100-ish feet down and you can see the bottom pretty well. So clear water, good light, and if the rocks at the bottom look like they could be smaller rocks closer to you it seems plausible that it could be 60 feet deep.

I don't see where refraction would fit into the picture. You're looking straight down perpendicular to the surface, refraction is experienced at an angle.
posted by zengargoyle at 6:26 PM on May 25, 2010 [1 favorite]

I think it's plausible. If you go somewhere where the air is exceptionally clear (I grew up in Alaska) everything looks way closer than it really is. The tops of mountains look maybe 100, 200 feet away. This effect is particularly distinctive when you're above treeline.

Our brains tend to cheat, and rely on two things to interpret distance:

1. The hazing effect of particulates (which is why distant mountains look misty)

2. Changes in scale of known items (the tiny speck of an airplane high in the sky)

When things are very clear, and there's nothing you can use to judge scale, your brain can play some real tricks.

This illusion is particularly strong above treeline, because your brain can't pick out the tiny dots of trees and judge distance that way. I don't see why the same wouldn't be true of a very clear pool of water, with the right kind of bottom.

It's also not the kind of lie a tour guide would tell. Tour guides kind of have an obligation to tell the truth about the natural world. If the guide had said "That pool contains monsters that will eat little children," then I might buy that they were trying to keep you from messing with it.
posted by ErikaB at 7:20 PM on May 25, 2010

Imagine two rays shooting from your eyes toward an object that you are looking
at. At your point of focus, where you can fuse the two separate images from your eyes
into a single image in your brain, the rays will intersect in a single point.

Now imagine that you are gazing directly downward into a pool of clear, deep water.
The two imaginary rays (really, all rays are imaginary) will enter the water, and if we
give them properties of light, will be refracted symmetrically.

Since the water has a higher refractive index than air, the path of the ray will steepen
relative to the path of the original ray, that is, it will proceed more directly to the bottom
of the pool than it would if there was no water. This means that geometrically, the intersection
of the two rays is rather deeper than it would be if there were no water in the pool.
This is the cause of the "Pool appears shallower than it really is." illusion.

Also note that this effect depends on how far your eyes are from the water surface,
relative to the distance from the water surface to the bottom of the pool. The closer your
eyes are to the water's surface (like, if you have you nose in the water), the less the
illusion of shallowness manifests itself.

I won't go all quantitative here, regarding dominant eyes, the distance between your
pupils, the distance to the water surface, the distance the bottom, or cerulean blue as
a cue to distance in atmosphere.
posted by the Real Dan at 7:25 PM on May 25, 2010 [1 favorite]

Is it possible that you, as a little kid, misheard the guide say "six feet" instead of sixty?
posted by The otter lady at 8:47 PM on May 25, 2010

I think what ErikaB is referring to "atmospheric perspective," or "aerial perspective" as first described by Leonardo daVinci. He was referring to air, although the effect would be the same in water. The point is, we see far distant objects (e.g. on the horizon) less distinctly because we're seeing them through a larger mass of air than close up objects. And of course if the air is hazy, they are even less distinct. If the air is exceptionally clear, the atmospheric perspective effect is lessened, and we think they're closer. In the same manner, the water, if clear, would make far off objects less distinct to a lesser degree than murky water.

But I don't think this is likely to account for the optical illusion. I suspect it is more likely that the lack of visual cues in a dark pool of water would disorient your depth perception.
posted by charlie don't surf at 9:12 PM on May 25, 2010

Is - [dramatic flourish] - this your cave?

There was the 'Baloney Pool'. Because the stream of water that flows thru the cave was so crystal-clear, an optical illusion made the small pools, which might be five or six feet deep, look as if they were only a fraction that deep. On one tour, the guide had stopped his group beside one of these tiny pools and was explaining how deep the water really was. The pool looked very shallow, nowhere near five or six feet deep. One of the tourists thought the guide was telling a tall tale, cried 'Baloney!', and stepped into the pool to prove it and found out the guide was right! The pool was thereafter known as the 'Baloney Pool'.

posted by ErikaB at 9:51 PM on May 25, 2010

Supporting evidence:

My Goggle-fu is failing me, but many of the astronauts who walked on the moon badly misjudged distance, at least at first. This is generally beleived to be because there is no haze on the moon to fade distance peaks, combined with a closer horizon.

I've been swimming off the coast of the Mediterranean in alarmingly clear water where the bottom looked only a dozen feet under the surface. After diving in it was pretty obvious that the sea floor was around 100 feet deep.
posted by Ookseer at 10:10 PM on May 25, 2010

I can't speak to the science of how deep water is vs how deep it looks, but when i was a lil' un i remember going on a tour of the Jenolan Caves in the Blue Mountains west of Sydney, and the tour guide told us exactly the same thing- there was a pool of perfectly still, beautifully blue water that looked maybe shoulder deep (to a wee one like myself) that he said in fact went 30 odd foot down. It might have seemed odd, but I definitely took it to be true at the time.. so either we both got taken in, or there's something to it..
posted by Philby at 2:49 AM on May 26, 2010

oh, and i, like you, immediately banished the thought of taking a dip in the lovely water and instead clung on extra tight to my dad's hand from thereon out..
posted by Philby at 2:51 AM on May 26, 2010

Once we dropped anchor in what we thought was a sheltered, shallow cove while fishing in the Torres Strait off the northern tip of Australia. I thought the water was no more than 6 feet deep as I could easily see a small ray on the sandy bottom, also clearly visible. The anchor dropped, and dropped, and dropped. And then the ray got bigger, and bigger, and bigger, until it was under the bow and its wings were on either side of the boat. I jumped in and tried to dive to the bottom - I couldn't.
posted by obiwanwasabi at 3:44 AM on May 26, 2010

I'll be dog -- maybe it was Diamond Cave I went to! I bet I did mishear the guide saying "six".
posted by Countess Elena at 4:39 AM on May 26, 2010

I bet I did mishear the guide saying "six".

I bet you didn't. If you ever go on a tour of something you actually know something about, you will hear the guides spouting the most *amazing* gibberish. Sometimes this gibberish will be prefaced with something like "one guy I gave this tour to said..." but often it isn't even that. The tour guides are reciting a script, they generally have zero knowledge of their own.
posted by DU at 6:19 AM on May 26, 2010 [1 favorite]

Just anecdotal: Near my hometown is this natural spring, called Kitch Iti Kipi. The water is remarkably clear, and 40 feet deep. I've been on the raft over this spring probably dozens of times and depending on the level of daylight it looks like it's no more than about 5 feet to the bottom. So IMO it's possible your tourguide wasn't pulling your leg.
posted by cuddles.mcsnuggy at 8:01 AM on May 26, 2010

Luray Caverns in Virginia has a similarly documented feature, but closer to 6 feet than 60.
posted by jrishel at 9:18 AM on May 26, 2010

Tour guides are variable. I was visiting Montezuma's Castle in Arizona with a friend that was fluent in French. The guide with French tourists was mostly talking nonsense. (my friend was native of Arizona, and knew perfectly well the nature of the place).

OTOH, as a child, I visited Kitchikipi Springs (spelling?) in Michigan's Upper Peninsula. The water is so clear (or was) you could see the springs bubbling up in the bottom, which, we were told, was 70 feet deep. You could see the fish swimming far below.
posted by Goofyy at 6:37 AM on May 27, 2010