Perspective, focal length and camera position

[Lindolfi]

Often it is said that focal length determines perspective in a photograph. With a telephoto lens, one compresses depth, while a wide angle lens creates converging lines and perspective "distortion"

We all have experience with this effect, but the conclusion that focal length determines the perspective in a photograph is not correct. The changing perspective is brought about by stepping away from the object when choosing a telephoto lens or getting closer when using a wide angle lens.

A simple experiment illustrates that only the position of the camera determines the perspective in a photograph.


Let us use a typical perspective object to photograph: the red-and-blue-chair designed by the dutch designer Gerrit Rietveld in 1918.


First of all we use two focal lengths (24 and 48 mm on fullframe) and at the same time adjust our position (by a factor of two) to keep the chair the same size in the image.




Now from this, you would think that it is the focal length that creates the difference in perspective. However, when we change both factors (focal length and position) independently, we get this:




(click here for a larger version)


As you can see, the focal length determines the part or angle of the world we see (changing from left to right in the figure), while position changes the perspective (rom top to bottom in the figure)


Pair 1-2 shows no change of perspective, although focal length did change
Pair 3-4 shows no change of perspective, although focal length did change
Pair 1-3 does show a change of perspective, although focal length did not change
Pair 2-4 does show a change of perspective, although focal length did not change

Pairs 1-4 and 2-3 do change in perspective, while focal length is changing, but that is due to the change in position.

(Under the figures, focal length in mm and distance to the middle of the chair in meter is given. The camera was on a tripod on constant height in all images. All images are uncropped)

[sebasj]

I ran a similar experiment, with similar results.

However, there's still the issue of focal length magnification, that I want to experiment. At these short distances, I assume there's not enough difference in distances between objects and camera to perceive the inherent maginification of the focal length.

I will see if I can try the same experiment outside, with elements at several distances from the camera, to see if the compression of planes is there or not and if it's product of the focal length or the camera position.

I am not sure if that would change perspective, but would give a different render of spatial perception.

Best,
Sebas.

[Lindolfi]

Thanks Sebas. If we call v1 the distance between the object to the front principal plane of the first lens and v2 the distance between the object to the front principal plane of the second (longer) lens. And if we call b1 the distance between the back principal plane of the first lens to the image plane and b2 the distance between the back principal plane of the second (longer) lens to the image plane, then the relation b1/v1=b2/v2 should keep the magnification equal in both images, even at short focussing distances.

You can either do this experimentally (measuring magnification), or measuring the positions of the principal planes of the two lenses with an optical bench and set up the camera accordingly in the two conditions.

Have fun

[rpcrowe]

I ran a similar experiment, with similar results.

However, there's still the issue of focal length magnification, that I want to experiment. At these short distances, I assume there's not enough difference in distances between objects and camera to perceive the inherent maginification of the focal length.

I will see if I can try the same experiment outside, with elements at several distances from the camera, to see if the compression of planes is there or not and if it's product of the focal length or the camera position.

I am not sure if that would change perspective, but would give a different render of spatial perception.

Best,
Sebas.

The apparent difference between crop formats and full frame formats usually results from different distances at which we shoot to get the same size image composition.

To fill a frame with a 50mm lens on a full frame camera; we need to be a lot closer to the subject that we would be to fill the frame with that focal length lens on a cropped format camera.