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.)

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