This may sound like a really dumb question, but I am trying my best to wrap my head around this and not having much luck.
Lets say I’m looking at a building down the block (or Jupiter for that matter.
If I look at it through some, 2x binoculars (ignore the fact that such a binocular may/may not exist for the moment), does the object appear “twice” as close? Hence, if the building down the street is 1000 ft away, it looks the same to me as if I was only 500 ft from it? That isn’t the way it works, is it?
Not exactly. 2X magnification means the object appears twice the size it does to the naked eye. Because of the inverse square law, an object twice as close appears four times the size.
An object twice as close does indeed appear to be twice the size. Someone hand me a roll of Charmin, cause pulling my head outta there is gonna be messy.
An object one foot away does not quite appear like an object two feet away would if it were magnified 2x. But for long distances, typical in a telescope or binoculars, yes it works that way.
A good illustration is Hitchcock’s “contra-zoom” technique, where the camera moves away and increases magnification at the same time. The two effects sort of cancel each other out, in the sense that the size of the object appears the same. But the perspective changes, so as the camera moves out the scene appears to lose its depth. More recently the technique was used in the Fellowship of the Ring - on the forest path as the black rider approaches (but still unseen).
Recall the simple relation: Hi/Ho = Di/Do Or, the ratio of the distance of the image (i) to the original image (o) equals the ratio of the height of the image (i) to the height of the original image (o). So, yes, 2x means it appears to be twice as close.