How does focal length change perspective? [duplicate]

Question

@MichaelClark answered a question I posted about zoom using focal length (emphasis added):

You are correct that a focal length twice as long (2X zoom) as the original one will make objects appear twice as tall and wide in a photo taken from the same location. The perspective of the picture taken from twice as far with 2X zoom will be different than the one taken from half the distance and the same focal length, though.

I don't really understand how those perspective changes would impact the produced image. A photo demonstration of this effect would really be helpful I think. Maybe the same picture taken once with twice the focal length and twice the distance and once with half?

Answer 1

If you think about it for a minute without the lens it should make sense. If you are standing near someone, they block a larger portion of your your field of view and so the background you see behind them is further out to the sides (because they block a larger portion of your field of view.

If you were standing right next to them, you wouldn't be able to see anything behind them since the side walls would be the first thing you see when you look around their head. If you back up on the other hand to be across the room, you have no problem seeing the wall behind them because they are further away and they don't block the entire back wall due to how much of your field of view they occupy.

When you translate that to a photo, the close up with a really REALLY wide angle would show their head with the side walls to either side. From across the room with a telephoto however, you'd see the window they were standing in front of behind them because they take up a smaller amount of the field of view compared to the wall behind them.

Answer 2

Let's assume you are 10 feet away from your friend Joe and take his picture in portrait orientation with a 50mm lens. Say there is a building 100 feet behind Joe. The building is 10X the distance from the camera as Joe is, so if Joe is 6 feet tall and the building is 60 feet tall they will appear to be the same height in your photo, because both would occupy about 33º of the 40º angle of view of a 50mm lens along the longer dimension.

Now back up 30 feet and use a 200mm lens. Your total distance from Joe is now 40 feet. Since you are using a focal length that is 4X the original 50mm (50mm X 4 = 200mm), he will appear the same height in the second photo as he did in the first. The building, on the other hand, is now 130 feet from the camera. That is only 1.3X as far as it was in the first shot (100ft X 1.3 = 130ft), but you have increased the focal length by 4X. Now the 60 foot tall building will appear to be roughly 3X the height of Joe in the picture (100ft / 130ft = 0.77; 0.77 X 4 = 3.08). At least it would if all of it could fit in the picture, but it can't.

Another way to look at it is that in the first photo with the 50mm lens, the building was 10X further away than Joe was (100ft / 10ft = 10). In the second photo with the 200mm lens, the building was only 3.25X further away than Joe was (130ft / 40ft = 3.25), even though the distance between Joe and the building was the same. What changed was the ratio of the distance from the camera to Joe and the distance of the camera to the building. That is what defines perspective: The ratio of the distances between the camera and various elements of a scene.