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Q: Visual appearance of a distant object ( Answered 5 out of 5 stars,   0 Comments )
Subject: Visual appearance of a distant object
Category: Science > Math
Asked by: hose7-ga
List Price: $20.00
Posted: 27 Jun 2005 00:59 PDT
Expires: 27 Jul 2005 00:59 PDT
Question ID: 537339
How does a person six feet tall appear at half a mile away, compared
with ten feet away ?  I want a quantitative answer.
Subject: Re: Visual appearance of a distant object
Answered By: elmarto-ga on 27 Jun 2005 06:13 PDT
Rated:5 out of 5 stars
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

The formula provided in that link is a good approximation, but not
exact. A more correct formula for angular size should be the

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) = 33.39

The same person, seen from a distance of 2,640 feet (half a mile) has
an angular size of:

2*arctan(6/5280) =  0.13

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

Google search terms
"angular size"

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!
hose7-ga rated this answer:5 out of 5 stars and gave an additional tip of: $10.00

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