Perspective and compression

Learning goal

You will be able to explain what decides the size of objects relative to each other in a photo, and manage this relationship by choosing where you stand. You will show that perspective comes not from the lens but from the camera's distance to the subject and the background; you will calculate on a face that an object's apparent size is inversely proportional to distance; you will explain why, when photographed from far away with a long lens, the background looks as if it has come closer to the subject and grown, and why, when photographed up close with a wide angle, it looks as if it has moved away; and you will know that a face's proportions depend only on distance, with the same physics on every skin.

The question

In a seaside town, you are photographing a portrait of a woman in a square with an old castle built on the slope behind it. In the first frame you shoot at 24 millimeters, from half a meter away: the woman's face fills the frame, her nose looks a little large, and the castle is a small, distant silhouette behind. Then you walk to the far end of the square and take a face of the same size with a long lens: this time the face's proportions are familiar, and the castle is right behind the woman, big, almost piled on top of her head.

Why does a long lens flatter a face? Whether a face is pleasing is a matter of taste, and this question has no single right answer. But there is a measurable explanation for why the two frames are so different, and the lens's share in this explanation is much smaller than people think. In this lesson we will find the source of the relationship called perspective, on a face and a castle, with simple division.

Context

In Lesson 12.1 we saw that when we cropped a frame taken with a wide angle from the same place, it looked very much like a frame taken with a long lens. The musician's lute looked huge with a wide angle too, because the camera was right up against it. These two observations point to the same truth: the size of objects relative to each other depends on where the camera stands.

Two expressions photographers often use tie this truth to the lens: it is said that a wide angle exaggerates and a long lens compresses. These expressions describe the effect correctly, but put the cause in the wrong place. Putting the cause in the right place lets you build the effect you want in a portrait or a landscape not only by changing lenses, but by changing place.

Simple explanation

What does apparent size depend on?

An object's size in a photo is inversely proportional to its distance from the camera: something that goes twice as far away looks half as big. This rule is independent of the lens; the lens only enlarges or shrinks the whole scene by the same amount. That is why the size of two objects in a frame relative to each other, that is their relative size, is decided by the ratio of the two objects' distances from the camera.

This point where the camera stands is called the viewpoint, sometimes written viewpoint / camera position. Perspective is the result of the viewpoint. If you shoot from the same viewpoint at 24 millimeters or at 200 millimeters, the objects in the two frames stand in exactly the same proportions to each other; the 200-millimeter frame looks like a piece cut out of the middle of the 24-millimeter frame. If you want to change perspective, you need to change not the lens but the viewpoint.

How do a face's proportions change?

On a face, the tip of the nose is roughly ten centimeters in front of the ears. Imagine the camera thirty centimeters from the nose: the ears are forty centimeters away. The ratio of the nose's and the ears' distances from the camera is forty to thirty; that is why the nose looks about a third bigger compared with the ears. The middle of the face looks swollen forward, and the edges look pulled back.

When you photograph the same face from three meters away, the nose is three meters away and the ears three meters ten centimeters. This time the ratio is a difference of about three percent, and the eye hardly notices it. To fill the frame with the face from three meters, a long lens is needed; but what corrects the proportions isn't the lens, it is the three-meter distance. It is plausible that many people find faces photographed from this distance more familiar, because people often look at each other from distances like this. This physics is the same on every skin; the nose of every face photographed up close grows, and the proportions of every face photographed from far away even out.

What do compression and expansion mean?

You can do the same calculation for the subject and the background. If the woman is two meters from you and the castle twenty meters behind her, that is twenty-two meters from you, the castle shrinks to one eleventh relative to the woman and stays a silhouette in the distance. Now imagine going twenty meters away from the woman and photographing the face at the same size with a long lens: the woman is twenty meters away, the castle forty, and the castle shrinks only to half relative to the woman. The castle looks more than five times bigger relative to the woman.

When photographed from far away with a long lens, the background looking as if it has come closer to the subject and grown is called perspective compression; when photographed up close with a wide angle, the background looking as if it has moved away and shrunk is called perspective expansion. The source of both is the viewpoint. The lens only lets you build the frame you want from that viewpoint: if you stand far away, you need a long lens to fill the subject; if you stand close, you need a wide angle to fit everything in.

How do you use this?

If you want the background to look big and close relative to the subject in a frame, step back and build the frame with a long lens. Houses lined up along a street seeming to lean on each other, a mountain rising right behind a village, the moon or the sun standing huge behind a silhouette are built this way. If you want the background to move away from the subject and the setting to look wide and deep, come closer to the subject and shoot with a wide angle.

In a portrait, the viewpoint decides the face's proportions and the size of the background together. When photographed from far away, the face's proportions even out and the background behind grows; this requires you to choose the background's color and brightness more carefully, because the background is now a bigger part of the frame. When photographed up close, the face comes forward and the background shrinks; this is useful when you want to tell of the setting the person is in. What you want the face and the background to tell decides which one you choose.

Visual evidence

You go back to the square of the seaside town. The woman is olive-skinned, middle-aged; on her head is a light-colored scarf fluttering in the wind. In the frame you take at 24 millimeters from half a meter, her nose is noticeably large compared with her cheeks, and her ears look pulled back; the castle, on the other hand, is a small stone silhouette behind her, above the rooftops.

In the frame you take at 200 millimeters from the far end of the square, about fifteen meters away, her face is the same size, but her nose, cheeks and ears are in their usual proportions. This time the castle behind rises right behind the woman's shoulders; the stones of the walls, the battlements and the gate can be made out. Because the castle is a background several times bigger than the face, you shift to an angle that leaves it in shadow in a way that brings the woman's face forward. The same woman, the same castle; what changed was only where you stood.

Common mistakes

Summary

Perspective, that is the size of objects relative to each other, comes not from the lens but from the viewpoint: an object's apparent size is inversely proportional to distance, and the ratio of their distances from the camera decides the relative size of two objects. Up close, the nose on a face can look about a third bigger than the ears, and from three meters this difference almost disappears; from far away with a long lens the background comes closer to the subject and grows, up close with a wide angle it moves away and shrinks. A face's proportions are decided, with the same physics on every skin, not by the lens but by distance; the lens only builds the frame you want from that distance.

Mini assignment

In this assignment you will measure perspective with your own eye by changing the viewpoint.

1. From the same place, photograph a scene at your widest and longest focal length; crop the wide frame, lay the two frames over each other, and see that the proportions stay the same.
2. Photograph a friend's face from half a meter with a wide angle, then from three meters with a long focal length at the same size, and compare the proportions of the nose and ears.
3. Photograph a scene with a subject in front and a distant building or hill behind, up close with a wide angle and from far away with a long lens, keeping the subject the same size.
4. In the frame taken from far away, change the color and brightness of the growing background by shifting a few steps to the side.

Check yourself

• Do the cropped wide frame and the frame taken with the long focal length show the same proportions?
• In the face you photographed up close, did you see the nose grow compared with the ears, whatever the skin color?
• In the frame you took from far away, did the background grow relative to the subject?

Glossary

Mini quiz

1. What really decides the size of two objects relative to each other in a photo?

• A) The ratio of the camera's distances to the two objects
• B) The lens's focal length
• C) The aperture
• D) The sensor size

2. If the camera is thirty centimeters from a face's nose and forty centimeters from its ears, how much bigger does the nose look compared with the ears?

• A) The same size
• B) Half the size
• C) About a third bigger
• D) Four times bigger

3. When photographed from far away with a long lens, why does a castle behind look big relative to the subject?

• A) A long lens enlarges only the background
• B) The ratio of the subject's and the castle's distances from the camera has become smaller
• C) The aperture has been stopped down
• D) The white balance has changed

4. In a portrait, what do you do so that a face's proportions look even, on every skin?

• A) Come very close to the face with a wide angle
• B) Lower the saturation
• C) Raise the exposure
• D) Stand a few meters from the face and build the frame with a long focal length

Answers

1. A — Apparent size is inversely proportional to distance; the ratio of distances decides relative size.
2. C — A ratio of forty to thirty means the nose looks about a third bigger compared with the ears.
3. B — Seen from far away, the difference in distance between subject and castle gets small compared with the total distance; the castle grows relative to the subject.
4. D — Distance decides proportions; from a few meters, distance differences shrink, and the long focal length only builds the frame.

Summary card

• Not the lens but the viewpoint decides perspective.
• Apparent size ∝ 1 / distance; relative size is the ratio of distances.
• From 30 cm the nose is ~⅓ bigger than the ears; from 3 m the difference is ~3%.
• From far with a long lens: the background grows and comes closer; up close with a wide angle: the background shrinks and moves away.
• Face proportions come from distance, with the same physics on every skin.

Bridge to the next lesson

All the numbers in this lesson were for a full-frame sensor: 24 millimeters wide, 200 millimeters long. But many cameras have smaller sensors, and the same lens catches a smaller part of the scene on these cameras. So does the number written on a lens describe the same thing on every camera? Is 50mm 50mm on every camera? The next lesson talks about the crop factor and how different sensor sizes change the same lens's behavior.