Photographic Perspective
Daniel I. Applebaum
21 June 1999

I originally wrote this article as a posting to the Nikon mailing list.

There's a lot of talk these days about perspective, cropping, film vs. CCD image area, etc. Although in this case, it was brought on by the D1 announcement, I think it would be good to clarify a few things about how photographic perpective works.

To try to clear up some confusion, I'll try to show that:

  1. Lens focal length does not affect perspective.
  2. Film size does not affect perspective.
  3. Location of the camera does affect perspective.

If you agree with 1-3 above, you probably don't need to keep reading. If you disagree, please continue reading, and dispute me where you see fit.

The linear size of the image of an object on the film is proportional to the focal length and inversely proportional to the distance of the object from the camera. So, when an object is twice as far away, we can use twice the focal length to get the same linear size.

So, say you are 1 meter from a soda can, using a 50mm lens. If you move to 2 meters away, using a 100mm lens will render the soda can the same size.

Now, let's add another soda can. You start at 1 meter from the soda can, using a 50mm lens. The second soda can is located 2 meters away. It appears to be half the size of the original soda can. Now you change to a 25mm lens. Both soda cans are now half the size that they appeared to be when using the 50mm lens. However, the relationship between the two soda cans has not been altered. We still have the same distance relationship to each can, so the only thing changed is the focal length.

If we simply cropped the 25mm film to encompass the same area as 50mm film, the images would be indistinguishable (ignoring imperfections such as grain and resolution limitations). In both the 50mm and 25mm images, the soda cans have the same relationship: the farther can is half the size of the nearer can. In the image, the cans have the same size relationship, so the perspective has not changed. (#1, above)

This cropping is identical to using a smaller film or CCD, or doing a crop later in the darkroom or digitally. The perspective doesn't change when simply reducing the film size. (#2, above)

Now, instead of swtiching to a 25mm, we continue to use the 50mm lens and double our distance to the nearer soda can, making the distance 2 meters. The image of the nearer soda can is now half the size as it was from our initial position. It is half the size because our distance doubled. However, the effect on the farther can is much different. Our distance to the farther can changed from 2 meters to 3 meters, which is not a factor of 2. Instead, the second can didn't become half the size as it was originally. It lost only 33% of its size.

So, the closer can lost 50%, but the farther can only lost 33%. The perspective changed. The image became flatter, because the cans, still the same distance apart, are closer to the same size in the image, even though we are still using the 50mm lens. By moving, we have changed the relative image sizes of the two cans. (#3 above)

We can now switch to a 100mm lens, to restore the size of the closer can. The closer can is now the same size it was in the first image. The second can, however is not the same size. The first can is the same size because it's 1/2 reduction from distance was countered by a 2:1 magnification. The farther can, however, was reduced 2/3 from distance, but gained 2:1 from magnification, so it is 4/3 of its original size.

So, the farther can is bigger than it was in the original image. In the original image, it was half the size of the closer can, and now it is 4/3's that size. So it is
1/2 * 4/3 = 4/6 = 2/3
Voila, still 2/3's the size of the closer can.

So, compensating for the distance change by using a telephoto does not change perspective.

Taking an extreme case, we get 1000m away from the nearer can. The farther can is then just .1% farther than the nearer can, so they appear to be almost the same size in the image, no matter which lens is used. Of course, we need to compensate the size of the closer can by using a 50000mm lens, in order to keep the closer can the same size as it was with the 50mm lens.