Hello hose7!
The "apparent size" of objects seen from a distance is called angular
size. This concept is widely used in Astronomy, and it also applies to
your question. For an simple explanation of what is and how to measure
angular sizes, please follow this link:
Basic Geometry - Angular size
http://boojum.as.arizona.edu/~jill/NS102_2004/geom.html#angularsize
The formula provided in that link is a good approximation, but not
exact. A more correct formula for angular size should be the
following:
Angular Size = 2*arctan( Size / 2*Distance )
(Remember that size and distance should be input in the same units).
Therefore, in your case, a person 6 feet tall, standing 10 feet away,
has an angular size of:
2*arctan(6/20) = 33.39º
The same person, seen from a distance of 2,640 feet (half a mile) has
an angular size of:
2*arctan(6/5280) = 0.13º
In other words, a person 6 ft tall, when standing 10 ft away, looks
about 256 times taller than when standing half a mile away.
Note from the formula that there is no linear relationship between the
size of the object and its angular size; however, as an approximation,
it can be said that an object seen from X times its current distance
will appear 1/X times bigger. That is, a person standing 20 ft away
will approximately appear half as tall as the same person standing 10
ft away.
Here's a link to an angular size calculator in case you're interested
in more cases:
Angular Size calculator
http://www.1728.com/angsize.htm
Google search terms
"angular size"
://www.google.com.ar/search?hl=es&biw=1003&q=%22angular+size%22&btnG=B%C3%BAsqueda&meta=
I hope this helps! If you have any questions regarding my
answer,please don't hesitate to request a clarification. Otherwise I
await your rating and final comments.
Best wishes!
elmarto |