0

I believe this question uses Angular Diameter to determine the answer but I'm not sure how to use it.

Question: If a widget is 10 meters wide and it is positioned 1,000 meters from the observer how wide will it appear?

Alternate Equation: At what distance will a widget that measures 10 meters wide appear to be 5 meters wide? (Maybe the alt question helps the first question become clearer)

Using this online calculator I inputted 10 meters for Linear Size and 1000 meters for Distance to Object. It returned an Angular Diameter of 0.572953020554149. But how does this help me determine the apparent size of an object at a given distance? Or alternately am I using the wrong formula?

Backstory: I can find many references to Angular Diameter on both Google and this forum. But I can't find one that explains how to use this simple concept to determine on object's apparent size.

DR01D
  • 113
  • you can only talk about this in terms of some sort of reference distance. An elephant at 100 meters will look to be the size of a horse at 30 meters and the size of a dog at 5 meters, or something similar. $\frac {\text {Width}}{\text{Distance}}$ remains constant. – Doug M Jan 31 '18 at 02:56
  • Awesome! How would I use that? Width/Distance? Is there an obvious ratio or equation that is appropriate for this simple idea? – DR01D Jan 31 '18 at 02:57
  • 1
    An object 10 meters across will have the same angular measure of an object 5 meters across when it is twice as far away. – Doug M Jan 31 '18 at 02:58
  • Ok interesting. So every time distance from the observer doubles the object should appear to shrink by 50%. Am I getting that right? – DR01D Jan 31 '18 at 03:00
  • That is it...... – Doug M Jan 31 '18 at 03:01
  • That's perfect common sense. But sometimes reality isn't that simple. Thanks! – DR01D Jan 31 '18 at 03:01
  • I would look up forced perspective on Wikipedia. I haven't checked the math, but they have some there to describe it. –  Jan 31 '18 at 03:12

0 Answers0