[Math] Using forced perspective to estimate the distance or size of an object

geometrypuzzle

Is it possible to use forced perspective to estimate the distance or size of an object if:

  • Both the top and the bottom of two objects are aligned, the size
    of both objects are known, but the distance between the objects is unknown.
  • Both the top and the bottom of two objects are aligned, the size
    of one object is known, the distance between the objects is as
    well, but the size of one object is unknown.

Appears angular size might be used to do the calculations, but really not sure.

Example: Here's an example of where "both the top and the bottom of two objects are aligned":

Example of forced perspective using the US coins penny & quarter

United States coins in photo:

  • Left, Penny Diameter: 19.05 mm (0.750 in)
  • Right, Quarter Diameter: 24.26 mm (0.955 in)
  • Distance: Unknown

Best Answer

If the quarter has about $1.273$ times the diameter of the penny but appears to be the same size then by similar triangles it will be about $1.273$ times as far away.

You need one of the distances to calculate the other distance.

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