I'm trying to understand Manishearth's experiment in the answer here,

To try this out, close one eye. Now hold your arms straight out, nearly stretched, but not completely stretched. Now extend your index fingers (there should be about one inch between them). Now try touching them together. Try this a few times, then repeat with both eyes open. You'll realise how necessary the second eye is for judging depth.

I tried the experiment a few times but I am really not sure what I am supposed to see/ how the experiment works.

The one part I do understand is the reason they have said not to completely stretch the arms. If one does that, then by the sensation of arm being stretched will give a sense of depth, so it is necessary to not extend till to total arm length.

P.S: I completely understand the mathematics and fact we need two rays, but I think I am not getting the correct result for the experiment. Ideally an answer with pictures would be best.

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    $\begingroup$ For the experiment you shouldn't focus on straight arms. Just close one eye, hold your arms in front of you with the index fingers pointing towards each other. Then let the index finger tips meet. You will miss much more when one eye is closed $\endgroup$
    – Steeven
    Aug 16 at 7:10
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    $\begingroup$ Hmm I mean, I have sense of where my fingers in space mentally, so I don't see how this experiment is supposed to give me some new insight @Steeven $\endgroup$
    – Buraian
    Aug 16 at 7:23
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    $\begingroup$ Yup! That sense is called proprioception. Basically, I am not surprised that the experiment is not giving you much insight :) You may need to try more challenging one-eyed attempts to see depth. Make sure not to move your eye or head, and make sure the object is not moving. $\endgroup$
    – Alwin
    Aug 16 at 7:26
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    $\begingroup$ @Steeven With eyes closed I can make the tips of my index fingers meet four time out of five. I can also make them meet behind my back two times out of three. Proprioception is very accurate and very instinctive. $\endgroup$
    – gandalf61
    Aug 16 at 7:57
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    $\begingroup$ @Filip Milovanović: Same here. This isn't at all a good demonstration of depth perception, it's a test of proprioception. $\endgroup$
    – jamesqf
    Aug 16 at 15:59

The problem with the two finger experiment is that your body’s sense of proprioception is so accurate and so instinctive that you don’t need binocular vision to touch your finger tips together. In fact, you don’t need vision at all. Try the experiment with your eyes closed. You will find that you can still touch your finger tips together quite accurately without even seeing them.

To get a better sense of the power of binocular vision, use a pen or pencil held in each hand instead of finger tips, to reduce the effect of proprioception. Wave the pens/pencils around to randomise the starting positions, and then try to make the ends of the pens/pencils meet. With both eyes open this task is very easy. With only one eye open you will find it is surprisingly difficult.

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    $\begingroup$ Interesting workaround. It helps if you hold the pens at random angles, in weird grips, or use pens of different lengths, to mess with your sense of spatial awareness. Even so, the effect may not be very pronounced, and your brain might make use of other ques, like shadows cast by a light source to the side (e.g. a window, a lamp). In my own attempts, the error was usually less than 2cm or so, and it looks like you can get better at it with practice. $\endgroup$ Aug 16 at 17:06
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    $\begingroup$ @FilipMilovanović: Yep. Tried it with pens and with fingers, and with 0, 1 or 2 eyes open. It's definitely easier with more eyes open and somewhat easier with fingers than with pens (especially if you change your grip on them before each attempt), but even with both eyes closed and pens held in weird grips I still seem to be rarely off by more than 1–2 cm. Proprioception is a pretty amazing thing. $\endgroup$ Aug 16 at 17:39
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    $\begingroup$ Ask someone else to hold two pencils in front of you. You direct that person how far forward/backward to move each pencil until they meet. $\endgroup$ Aug 16 at 19:50
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    $\begingroup$ @IlmariKaronen, it's not just proprioception. Your brain's got various single-eye depth cues (eg. how hard your eye's warping the lens to get things in focus), but for close-in work, the two-eye cues of stereopsis and convergence are much more effective than anything else. $\endgroup$
    – Mark
    Aug 16 at 21:04
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    $\begingroup$ @stackoverblown: Better yet, just try to touch a stationary object (e.g. the edge of your computer screen) with your finger. It's definitely a lot easier with two eyes open than with just one, especially if you change the distance between the object and your body before each attempt. $\endgroup$ Aug 17 at 8:03

You do not need two eyes to determine depth, although having two eyes certainly helps.

There are many ways to retain depth perception with one eye. See here: https://en.wikipedia.org/wiki/Depth_perception#Monocular_cues

Two rays is necessary, but you can attain two rays with one eye given special circumstances, by moving your one eye to two places, for example.

It is not uncommon for people to try this experiment and find that they have a fine time with depth perception with one eye closed.

In fact, you might even have a fine time doing this with both eyes closed, using your sense of proprioception. Better to try identifying a depth to an object which is not your own body. https://en.wikipedia.org/wiki/Proprioception

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    $\begingroup$ as someone who has had persistent double-vision since childhood, and generally suppresses one image, it's surprising how good you can get with just a single image. The fact that I suppress one image and so have weaker depth perception than average is pretty much only noticeable in a few precision task e.g. catching a ball. For everything else I do just fine based on the various monocular cues mentioned in the wikipedia page (especially accommodation and parallax) $\endgroup$
    – Tristan
    Aug 16 at 16:25
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    $\begingroup$ I came here to add to this answer as well - As someone with a controlable 'lazy eye' (I can intentionally induce 'double vision' to see a wider range while ignoring what is directly infront of me, I often use the above ideas of 'Monocular cues' every day in my life - it means that if a contact lens falls out of my eye, I can continue driving without any issue/concern with a single eye, but I can try to use both if not tired. $\endgroup$
    – Cinderhaze
    Aug 16 at 17:11
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    $\begingroup$ For another example, I'm just old enough to need the contact lens equivalent of bifocals: one lens selected for long-distance vision (as normal) but the other for around half a metre.  (I found this surprisingly easy to get used to.)  This gives good vision at nearly all distances, without needing reading glasses or whatever.  At many distances, only one eye has sharp vision, so you'd think I'd have problems judging depth — but I haven't noticed any.  I guess this shows how many other cues we use for depth perception. $\endgroup$
    – gidds
    Aug 16 at 21:15
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    $\begingroup$ Another monocular person here. My right eye is extremely short-sighted, I don't get on with glasses, and my eyes don't produce enough lubrication for "normal" contact lenses, so I spent 40 years working with one eye. A few years ago that eye started losing it too, and coincidentally silicone disposable lenses became available at the same time. The change in vision was pretty profound - suddenly depth really existed! :) But up to that point I had been judging vehicle speeds and distances, playing racquet sports and so on perfectly well with just a single eye and monocular cues. $\endgroup$
    – Graham
    Aug 17 at 10:43
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    $\begingroup$ Another example— This is why my rabbit bobs her head to get depth perception. $\endgroup$ Aug 18 at 5:05

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