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Q: Visual appearance of a distant object ( Answered ,   0 Comments )
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 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.```
 ```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```