Is there a uniform 'shrinkage' of an object when one moves away from it?

Question

By this, I mean does an object's apparent size decrease at a set rate? For instance, does an object of 100 feet length/height appear smaller on a regular scale, and, if so, can knowing the object's true size enable one to judge their distance from it?

Answer 1

If you know the size of an object by measuring the subtended angles you should be able to work out the distance. Don't ask me to do it , it's been nearly 50 years since I was at school.

Answer 2

Yes, there is a set rate for the change in apparent size of an object as it gets further away.  If you want to know more about exactly how it works, I would suggest looking up the mil distance approximations that are used by US army snipers.  Using set mil ticks on their scopes they determine the apparent size of the object and then compare it to the known mil size at a certain distance.  I don't know off hand what the equations used are, if it just a directly inverse relationship between distance and size or not, but it could easily be found by searching for sniper distance approximation methods.

Answer 3

Yes an object substends at rate of the inverse square law.

move twice as far away and the area is quartered.  Three times away and the area is 1/9th.  Five times away and the area is 1/25.

If you are looking at an actual square, set it at 10 feet away.  What ever the side dimension is (example of 4 feet so area is 16), move to 20 feet and the sides are 2 feet and area is 4).

We use reduced size targets when shooting at closer ranges so that the error is about the same in terms of angles.

Answer 4

It is also necessary to know how the eye works: it has a lens with adjustable curvature. When we try to observe object, the curvature is automaticly set to focus all rays coming from the same point to the same point on the retina (the back of the eye with light detecting cells). So all light from one point is focused to one point. All light from another point will be focused to another point. If the angle between source points is greater, then they will focus further apart. So the apparent size of the object depends on the angle between it's most distant points, which decreases with distance.