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I also asked this on StackOverflow but this is a better place to ask the question.

Suppose an object of 4cm is right in front of my eyes. I move it further away till it appears to me to be of 2cm. Is there a way to find out how much I moved it?

I tried using the concept of similar triangles, but, we need to have another length given to us to calculate the distance.

Another idea I thought was to use the focal length of the eye. But, couldn't find a way to use it.

EDIT: I think it would be more clear if I give an example. Suppose I close one of my eyes and put my thumb above the nose (the distance of the thumb from my eye is close to 0) and I measure the length of my thumb to be 4 cm. Now, as I slowly move it away from me, the length of the thumb from my eye appears to be smaller. Suppose this height from my eye becomes 2cm at some distance x (from my eye). I want to calculate x.

Shauryagoel
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    What do you mean by "it appears to me to be of $2$cm"? Presumably, this means it appears the same size as some $2$cm object held at some particular distance from you, but what particular distance? – Gerry Myerson Jun 13 '20 at 01:43
  • @GerryMyerson Yeah, it means that from my eye it appears to be of 2 cm (in reality it is 4 cm). I have to calculate the distance I moved that object. – Shauryagoel Jun 13 '20 at 02:02
  • The size of an objects apparent area decreases with the square of distance so, if it looks half the diameter, it is one quarter the apparent area and thus twice as far away. That is, it is twice as far away as whatever "right in front of my eyes" means. If it looks to be only half the area, then it is $\sqrt{2}=1.414...$ times as far away/ – poetasis Jun 13 '20 at 02:40
  • You haven't told me what it means to appear to be $2$cm. Put it this way – at what distance does a $4$cm object appear to be $4$cm? – Gerry Myerson Jun 13 '20 at 07:53
  • @GerryMyerson An object of 4cm would appear to be of 4cm when it is just in front of my eye (thumb above the nose in the example). – Shauryagoel Jun 13 '20 at 13:35
  • OK, let "close to zero" be $r$. Then the length will appear to be $2$cm when the distance is twice $r$. [Of course, the problem here is that since your thumb is $4$cm long, it can't all be at a distance from your eye of "close to zero". Some part of your thumb will have to be at least $2$cm from your eye.] – Gerry Myerson Jun 13 '20 at 23:11
  • Any thoughts about what I've written? – Gerry Myerson Jun 14 '20 at 23:46
  • I guess you've lost interest. – Gerry Myerson Jun 17 '20 at 07:44

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