Telephotography of restricted areas
Dreaded Trigonometry
I promised no diagrams. So sue me. Luckily, all you need to remember
from middle school are the properties of similar triangles. Similar
triangles have the same angles. Their dimensions will be ratios of each
other. So we have:
[Focal Plane] / [Field of View] = [Focal Length] / [Distance to Target]
This diagram works for horizontal or vertical field of view provided
you use the proper dimensions for the focal plane. For 35mm film, the
focal plane is 24mm vertical by 36mm horizontal. For a DSLR, consult
your manual.
Examine the photograph below. If you took the new hangar and used it as
a ruler, the image would measure 4.33 "hangars" wide. From satellite
imagery, the new hangar measures approximately 200ft x 500ft. However,
the camera's view is not parallel to any surface of the hangar. We can
approximate the "frontage" of the hangar presented to the camera by
using the hypotenuse. [The diagonal for the trigonometric
challenged.] That would be 539ft. Multiply by 4.33 "hangars" to
get a field of view is 2335ft, or 712 meters.
Focal Length = [Distance to Target] * [Focal Plane] / [Field of View]
Focal Length (meters) = 42000meters * 0.036meters / 712 meters = 2124mm
.
Plug the results into FCalc for a sanity check:
Close enough for government work.