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Name: Stephen
Status: other
Grade:
Location: N/A
Date: June 2008

Question:
If I have an object that is a give size, let us say one meter square, and looking at it from an unknown distance it only appears to be say 5 cm square. Is there a formula to work out the distance from the given object?



Replies:
Stephen,

If you had a precise way of measuring small angles then you could sight on the bottom of the object and then sight to the top measure the angle of of traverse between bottom and top. Knowing the angle and the actual height of the object and assuming a 90deg angle from the bottom edge to the top of the object, than distance = object height / tangent of the height.

Greg (Roberto Gregorius)


Answer: First Google "size constancy" were in is noted that apparent size tends to be constant despite viewing distance, i.e. size appearance does not correspond to changes in the size of the retinal image (which is geometry).

However, from a stimulus stand point, things are often quantified as visual angle and the formula is Visual angle = arctan (object size/object distance). A handy thing to remember is that one meter at 57 meters is one degrees. One inch at 57 inches is one degree. One mile at 57 miles is one degree. Etc. Another useful factoid is that arms are about 28in (eg half of 57 inches) and people usually have a finger that's about 0.5inches wide. So, if you hold up that finger at arm's length it is about one degree AND ANYTHING AT ANY DISTANCE THAT IS VISUALLY BLOCKED BY THAT FINGER IS ALSO ONE DEGREE. (Give some thought to circumstance.)

Michael Loop



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