Optical illusion in the mountains ― can someone explain?

[Heroique]

There’s an optical illusion that fascinates me, and I think other landscape photographers will know what I’m talking about.

When I climb high, and view nearby mountains, it seems they’re lower than I am, when it’s really just the opposite.

Below is an example – and perhaps you can share examples, too.

I’m in the Olympic Mountains (Washington state) – I’ve set-up my tripod at 3,800 feet. Now, take a look out there. Seems I’m at a higher elevation than anywhere else in the neighborhood. Yet, those snow-clad mountains (one of which is Mount Olympus) rise to 8,000 feet. In other words, I look higher, but I’m a good 4,000 feet lower! (I should add that my camera is perfectly leveled.)

I have a couple of guesses why, but I want to hear from the scientists first.

Tachi 4x5
Schneider XL 110/5.6
(Lee orange filter)
Polaroid Type 55
Epson 4990/Epson Scan

[TheDeardorffGuy]

And how faraway is Mt. Olympus?......................

[Frank Petronio]

Those snowy peaks look higher than you are to me. You're only talking a couple of degrees difference here and the curvature of the Earth is probably eating half of that up alone. The other half might be the mushrooms you ate on the hike or something?

[Heroique]

And how far away is Mt. Olympus?

Mount Olympus is about 17-18 miles away.

The nearby ranges are close to my elevation – so they add to the mystery, too. Some of them rise a few hundred feet higher than my location. Yet I seem to be looking way over all of them.

[Darin Boville]

I'm with Frank. The tall mountains in the distance seem above the halfway line of the image--thus should be higher than the viewpoint? Nearby peaks look to be in the same ballpark as the viewpoint.

--Darin

[Heroique]

Here’s an example to help compare – Mount Adams in the Cascade Range.

I’m 10 miles away, at 3,000 feet, and Mount Adams is a 12,000 foot mountain. So in this example, I’m considerably closer to the mountain, I’m about 1,000 feet lower than before, but this mountain is much, much higher than Mount Olympus. The midrange mountain is several hundred feet higher than my tripod location.

Another leveled camera, but it’s my 240mm lens this time.

Tachi 4x5
Fuji A 240mm/9
(w/ Lee orange filter)
Ilford FP4+ (in D-76)
Epson 4990/Epson Scan

[Mark Sawyer]

I have a couple of guesses why, but I want to hear from the scientists first.


This isn't so much from a scientist, but from someone who flew hang gliders on a significant level (on the cover of the national Hang Gliding mag a couple of times in the 90's...). At high altitudes, your mind substitutes cloud base for the horizon it doesn't see, and cloud base can be a lot higher. We judge altitude at a great distance against the horizon. You're judging against a false horizon. That's about it.

[Heroique]

That’s really interesting, I’ve never heard that but it makes sense. It may play some sort of role in the first shot since the distant air towards the horizon contains such a thick dose of hazy, rain-forest moisture.

[Mark Sawyer]

It used to be a "well known" among pilots, because it could fool you as to your real altitude. But these days, everyone relies on a digital altimeter, spitting numbers at you...

[Frank Petronio]

Well then the true Horizon is 8000' under those mountains ;-)

[Brian K]

Here’s an example to help compare – Mount Adams in the Cascade Range.

I’m 10 miles away, at 3,000 feet, and Mount Adams is a 12,000 foot mountain. So in this example, I’m considerably closer to the mountain, I’m about 1,000 feet lower than before, but this mountain is much, much higher than Mount Olympus. The midrange mountain is several hundred feet higher than my tripod location.

Another leveled camera, but it’s my 240mm lens this time.

Tachi 4x5
Fuji A 240mm/9
(w/ Lee orange filter)
Ilford FP4+ (in D-76)
Epson 4990/Epson Scan

Here's a simple thing to remember, when things are far away from you they look smaller, even really big things.

[Steve M Hostetter]

You see mountains behind taller mountains which in my mind is do to refraction or the bending of light rays..

[Kevin Crisp]

Things that are further away look smaller. All parts of things further away look smaller. Not as wide, not as tall. This leaves you unable to judge their relative height by size alone as you move further away, though snow line and tree lines can give visual clues.

If it didn't work this way -- things look smaller as you move away but not on their vertical axis -- you'd be seeing a soaring, extremely skinny mountain, A great distances they would look like skinny but extremely tall pillars.

The curvature of the earth would take a little, maybe 30 feet from a distance of 20 miles, but not enough to be a factor.

[Struan Gray]

Things that are further away look smaller.

There is a further factor, which is that our binocular vision becomes pretty inaccurate beyond a hundred meters or so, and fairly useless after a kilometer/mile. This makes the assessment of size fraught with error. K2 is famously K2 and not K1 because a closer mountain (Masherbrum) appeared taller to the original survey team.

We actually use the fact that things look smaller as they get further away - and clues from leading lines in the landscape - to compensate, but that means you can easily be fooled by terrain. Marksmen, for example, learn to mentally adjust their impressions of distance if the ground between them and the target is not flat - a valley makes distant objects look closer.

Once you get beyond the middle distance, your brain starts telling you fairy stories. A classic is the way that a sunburst through clouds (or crepuscular rays) appear to diverge away from the sun. In fact, the light beams are very nearly parallel, it's just that we do not perceive their varying distance - our brains prefer to see a set of diverging rays. Mountain shadows are almost always triangular, whatever the shape of the mountain, for the same reason.

[Bill_1856]

I can't speculate about the illusion, but that first picture is very nice. Thanks for posting it.

[Paul Metcalf]

Once you get beyond the middle distance, your brain starts telling you fairy stories. A classic is the way that a sunburst through clouds (or crepuscular rays) appear to diverge away from the sun.
X2. Another one is that the size of the (full) moon appears bigger when it's near the horizon compared to when it's further up in the sky.

I think there is also some optical illusion going on with the use of a 110 (WA) compared to the 240 in your second photo.

[Nathan Potter]

I think to a first order the illusion is perspective distortion as implied by some above. A switch to longer tele lenses for the particular format will reduce the effect of the illusion. But if I look at your first image I agree with Frank, the distant peaks don't seem lower because I tend to automatically correct my vision for such a perspective effect just due to experience.

Nate Potter, Austin TX.

[Vaughn]

It is not an optical illusion, it just looks like one...

[tgtaylor]

"Relative size - If two objects are known to be the same size (e.g., two trees) but their absolute size is unknown, relative size cues can provide information about the relative depth of the two objects. If one subtends a larger visual angle on the retina than the other, the object which subtends the larger visual angle appears closer."

-Wikipedia.

[Scott Knowles]

If you extend the line of sight from you (camera base) to the distant mountains it's likely you'll see it's below the peaks (accounting for any slight curvature of the earth) and the angle between the base and the peak would determine the elevation difference. It's similar to plane-table surveying and mapping used in the 1900's, see photo (http://online.wr.usgs.gov/outreach/historicPhotos/enlarged/shortie_clark.html) from USGS.

[Heroique]

I think there is also some optical illusion going on with the use of a 110 (WA) compared to the 240 in your second photo.


A switch to longer tele lenses for the particular format will reduce the effect of the illusion.

Interesting, I mentioned the 240mm lens since I thought it might be an important variable in the height-illusion of the Adams shot, but the 110mm might have played even larger role in the Olympus shot.

However, it occurs to me how problematic it is to try to describe this relative height-illusion w/ any photo, since a level camera’s photo gives a frame of reference that explains & dispels the illusion to some degree. (For example, Darin naturally makes use of the film’s “half way line.”) But there’s no way I would try to conjure this illusion for you w/o a photo! The middle way, I suppose, is to try to examine the photo while “extending” its four sides beyond your peripheral vision – to better imagine the scene, that is, as if you were viewing it w/ the unaided eye...

(BTW, one of the “guesses” I was withholding, in deference to the scientists, was the relationship between the actual & perceived horizon lines, and how this relationship changes not only w/ altitude, but with the prevailing topography.)

-----
The remark about what happens to our brain & binocular vision, as distance increases, is revealing and helps explain to me the following:

In the Mount Adams shot (below again), you can see the snow line and how far down the mountain it comes. My location is much lower than that snow line. Estimating where one would be standing on Mount Adams, at my tripod elevation, jars w/ first impressions. Usually does in mountain-high situations like this.

[tgtaylor]

"...If one subtends a larger visual angle on the retina than the other, the object which subtends the larger visual angle appears closer."

-Wikipedia.

A tall building appears taller when you're up close because it subtends a larger visual angle on the retina than when the same building is more distant as the visual angle on the retina is then smaller.

Thomas

[Mike Anderson]

...(I should add that my camera is perfectly leveled.)...

What is the precision of the accuracy of the perfection of the leveledness of your camera?

:)

...Mike

[paulr]

TAt high altitudes, your mind substitutes cloud base for the horizon it doesn't see, and cloud base can be a lot higher. We judge altitude at a great distance against the horizon. You're judging against a false horizon. That's about it.

That's interesting.

I also concur Struan's point. The scale of the mountains messes with our human sense of scale. I have much more fear of heights on urban fire excapes than on cliffs, because looking down, seeing little cars and fire hydrants and people, it's clear that I'm up higher than i belong. In the mountains, even a couple of thousand feet off the deck, everything's overwhelming and odd looking. It's hard to tell if the green stuff is shrubbery or hundred foot pine trees, and it's impossible to tell if the rocks are the size of gravel or houses.

I once ended up perched with a climbing partner on a chockstone in a chimney in the Tetons. We were retreating off-route from a climb. We'd already rappelled several rope lengths and the chimney was overhung and we had no idea if the ropes would reach to the boulder field below us. It looked as if we could have been a hundred feet up ... or five hundred. I drew the short straw and pitched off, with all kinds of prussic cord so I could fight my way back up if need be. It turned out we were barely more than fifty feet off the deck. Most of the rope was in a big lazy heap right below us. It was funny and we felt ridiculous.

[Greg Miller]

It is simply perspective (see attachment)

[paulr]

It is simply perspective (see attachment)

Shot glass, pint glass, yard.

So the OP sees it that way because he's been drinking?

[bsdunek]

This isn't so much from a scientist, but from someone who flew hang gliders on a significant level (on the cover of the national Hang Gliding mag a couple of times in the 90's...). At high altitudes, your mind substitutes cloud base for the horizon it doesn't see, and cloud base can be a lot higher. We judge altitude at a great distance against the horizon. You're judging against a false horizon. That's about it.

A good explaination. I fly small planes, and see the same effect. The false horizon can get you in trouble if you don't keep your mind working.

[D. Bryant]

The other half might be the mushrooms you ate on the hike or something?

You beat me to it Frank!:)

[Greg Miller]

Shot glass, pint glass, yard.

So the OP sees it that way because he's been drinking?

LOL

I was too lazy to draw mountains so I used stick figures instead... pretty interesting how you turned that into drinking vessels though :p

[Heroique]

I can’t speculate about the illusion, but that first picture is very nice. Thanks for posting it.

Thanks Bill, I missed this the first go around.

It was a fun day, and I pitched a tent that night.

[Heroique]

From someone who flew hang gliders...


I once ended up perched with a climbing partner in the Tetons...


I fly small planes...it can get you in trouble if you don’t keep your mind working.

I’m feeling akin to these people who explore the sky and notice curious perceptual changes.

-----
I also recognize this topic will, naturally, attract the stay-at-home drug addicts, and their comments are also welcome! ;^)

[ic-racer]

Is your lens centered vertically? (all 4 crescents of light the same size peeking through the corners)

[jnantz]

weather / barometric pressure can add a magnification-factor as well.

[Heroique]

Is your lens centered vertically? (all 4 crescents of light the same size peeking through the corners)

Hi ic-racer,

In each shot – Mount Olympus & Mount Adams – the camera was leveled and its movements neutral. My 110mm for Olympus, my 240mm for Adams, both times centered.

One key problem is that the two shots – or any shot I might show – vitiate the real-life illusion; however, they still communicate enough of its impact to try to show & discuss here. Keep in mind I’m referring to the “relative-height” illusion (observed from an elevated location), not to the other types that have naturally come up in this discussion.

The more helpful posts have explained the illusion pretty well to me, if not perfectly well. I might pull-out some physics & weather books to complement the interesting observations here.

[tlitody]

How are you measuring your altitude?
If you are using a pressure altimeter, did you calibrate it that day at a known height and was the weather pressure constant that day?

[Heroique]

How are you measuring your altitude? If you are using a pressure altimeter, did you calibrate it that day at a known height and was the weather pressure constant that day?

I’m very old fashioned – paper maps w/ topographical lines for me.

With an oriented paper map, it’s easy (for me) to compare its technical information about altitude w/ my “sense” of the surrounding land. Sometimes, the correlation isn’t so simple, which is of course the subject of this thread.

Others might have more to say about fancier gadgets.

If you’re interested, there’s a thread titled LF hikers ― is “Map & Compass” a dying art? (http://www.largeformatphotography.info/forum/showthread.php?t=72873&highlight=hikers
) that I remember.

[tlitody]

I’m very old fashioned – paper maps w/ topographical lines for me.

With an oriented paper map, it’s easy (for me) to compare its technical information about altitude w/ my “sense” of the surrounding land. Sometimes, the correlation isn’t so simple, which is of course the subject of this thread.

Others might have more to say about fancier gadgets.

If you’re interested, there’s a thread titled LF hikers ― is “Map & Compass” a dying art? (http://www.largeformatphotography.info/forum/showthread.php?t=72873&highlight=hikers
) that I remember.

I agree a good map and compass combined with a sense of direction and ability to read terrain and match it to a map is the way to go.
But sometimes we get it wrong and altitudes on maps are not always correct. An altimeter correctly calibrated on the day is a handy check. I would never rely on electronics 100%.
Three times I have had to correct a group leader due their inability to correctly interpret a map and were getting the group lost. On one of those occasions I used an altimeter to confirm we were on top of a different hill than they thought we were.
Fortunately I had calibrated it that morning. So you see, it's easy to be mistaken.

[jp]

I'm coming from the perspective of someone who has spent 7 summers on a boat on the ocean, sometimes in fog. You basically have too look for where the horizon is. It's not intuitive when weather obscures things. For me, that's where the other boats and buoys come from. On a mountain, that's what's level. If the "horizon" is not level, then you have to look for the lowest spot on it with nothing behind it, and that's your best estimate of where the horizon is. Now, I work on towers at hilltop sites. We have to accurately downtilt antennas. We often have to tilt it down a bit more than we estimated simply because it's easy to be off a degree or two by quickly eyeballing where the horizon is, as has been shown here, caused by other things blocking our view to the actual horizon.

[Greg Miller]

The first attached image shows a red line at the center of the image. The OP said his camera was leveled, so the horizon and the tall mountains are placed where you would expect them. Given the use of a wide angle lens (diminishing the size of distant objects), and given the distance that the tall mountains are away from the photographer, the summits are about where you would expect them to be - that is very slightly above the center/horizon line.

But the horizon also seems to not be level, tilting from left to right. I rotated the image to render what appears to be a more level horizon (attachment 2). To my eye, this negates any feeling that the distant mountains are lower the the near mountain. The far mountains are just that - far away - and there fore very difficult to judge size or height.

[Heroique]

I think your observations are good ones, Greg. It’s interesting to see how we work w/ our unaided senses in the wild & on our photos back home, each in an effort to make things seem “right.” One interesting thing I should add about this landscape shot is that the mountain ridges, near and far, generally are trending downward to the right, mainly because these river valleys are all flowing in that direction, carrying their burdens of heavy rain water & eroded soil to the nearby Pacific Ocean; it’s not a perfectly consistent trend, and describing the land is difficult – but one might imagine the Olympic Range as circular w/ rivers running radially. (I almost said “radically,” because this downward elevation trend helps make the principal Olympic Rivers ferocious.) I suspect most people would, naturally, want to “fix” the land so it’s more level – I certainly do. Way up here, comparing my unaided senses to my maps keeps reminding me that no matter how much I think I “know” a landscape, I can usually count on it to “trick” me to some degree. Especially if I’ve traveled into it from a very different one. Now I’m tempted to scan and share my topographical maps!

[Greg Miller]

I figured that may be the case; so I purposely said "seems to be" rather than "is". A range that is level can also appear to be not level if it is not perpendicular to the camera as well - the part of the range that is further away will appear to be lower than the part that is nearer. More perspective stuff..

[jp]

www.heywhatsthat.com is an interesting website that shows an exagerated horizon and the height of all the peaks or landmarks visible from a particular location. One of my customers makes this site. We use it for radio tower purposes. The visibility cloak puts a red mask over what is visible from the location which is quite handy too.

[Leonard Evens]

It is simply perspective (see attachment)

As a mathematician, let me confirm his explanation. The "science" behind this is the fact that what you see and what is recorded on film is the angular displacement of the top of the distant mountan above the line of sight. Ignoring the curvature of the Earth for the moment, you can see that this angular displacement gets smaller as the distance to the mountain increases. That is why, for example, you can entirely block out a high mountain, by putting a few inches of your hand in front of your eye.

[Jehu]

The curvature and refraction should amount to about 186 feet at 18 miles. I've used 4.25 seconds of arc per 1,000 feet as a rule of thumb several times and it's always been pretty close.

Signed: a Land Surveyor

[jb7]

As a mathematician, let me confirm his explanation. The "science" behind this is the fact that what you see and what is recorded on film is the angular displacement of the top of the distant mountan above the line of sight. Ignoring the curvature of the Earth for the moment, you can see that this angular displacement gets smaller as the distance to the mountain increases. That is why, for example, you can entirely block out a high mountain, by putting a few inches of your hand in front of your eye.

Or...

http://www.youtube.com/watch?v=8vbd3E6tK2U&feature=youtube_gdata_player

[Heroique]

Mount Olympus is about 17-18 miles away.


The curvature and refraction should amount to about 186 feet at 18 miles. I've used 4.25 seconds of arc per 1,000 feet as a rule of thumb several times and it's always been pretty close. Signed: a Land Surveyor.

Nice.

Not just the “186 feet.”

But the pure calm of mathematics.