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A thought experiment between a friend and I.

Let's say I'm 6ft tall, and I have a friend who's 7ft tall.

To keep things very simple for the sake of discussion, we're on a flat level plane, and I have a dumpy level.

At first, my friend is nearby, and his head is above my eye-level as determined with the dumpy level.

But as he moves away, he appears smaller and smaller.

As far as Perspective goes, how far does he have to go before he appears entirely below my eye-level according to the dumpy level?

Jesse Gordon
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The answer is that on a flat level plane, your friend will be taller than you at any distance. The top of his head will never appear below eye-level.

If he is far enough, his head may be so small that you can no longer see it as anything but a dot, and that dot may appear at eye-level but never below.

The angle to the top of his head is equal to the arctan of his height above your height divided by distance, and because his height is always positive compared to yours, the angle will always be positive, even if it is such a small angle your eyes cannot resolve the angle, it is still a very small positive angle, which means your friend will never appear below you at any distance.

Jesse Gordon
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    To view it in another way, the eye level is on the axis of the view cone (this cone is what leads to the perspective effect), so if you look horizontally, this axis will never be higher than the altitude at which the eye is located. – Ruslan Nov 27 '21 at 00:13