Focal length

Learning goal

You will be able to explain what the millimeter value written on a lens describes, and predict how much the frame will widen or narrow from the same place with a given focal length. You will define focal length as an optical distance between the lens and the sensor; you will see how this distance, together with the sensor size, decides the angle of view; you will calculate that when the focal length doubles, the subject appears twice as big in the frame; you will read the two numbers on a zoom lens; and you will know, as true on every skin, that in a portrait focal length changes not the face's proportions but where you need to stand.

The question

In a fishing harbor, you are standing at the end of the pier. First you shoot with a 24-millimeter lens: the whole harbor, the boats, the lighthouse and the sky fit into the frame. When you switch to 50 millimeters from the same place, the frame narrows; now only the deck of a boat gathering its nets is visible. When you go up to 200 millimeters, only the face of the young fisher on the boat and the hands holding the net are left in the frame.

What do 24mm, 50mm and 200mm mean? These numbers don't describe a lens's length, weight or quality. In this lesson we will talk about what these millimeters measure, why they widen and narrow the frame, and why the same number can give a different image on different cameras.

Context

In Lesson 4.6 we saw that the cameras on the back of a phone are named with numbers such as 0.5x, 1x and 3x, and that these numbers describe an angle of view relative to the main camera. On interchangeable-lens cameras the same information is written in millimeters. In Lesson 10.8, too, when calculating the safe shutter speed, we talked about how focal length magnifies the hand's shake, and how on a small sensor you need to think with an equivalent number.

This module looks at lenses themselves. We will talk in later lessons about which lens is good for what, the difference between prime and zoom lenses, and the flaws and care of lenses. At the base of all of them is the single number in this lesson: focal length. Reading it correctly means knowing what you are doing when you choose a lens or turn the zoom ring while shooting.

Simple explanation

What does focal length measure?

A lens gathers the rays coming from a point at infinity into a single point on the sensor. Focal length is the optical distance at which this gathering happens; roughly, you can think of it as the distance between the lens's optical center and the sensor. It is written in millimeters: in a 24-millimeter lens this distance is short, in a 200-millimeter lens it is long.

This number isn't the physical length of the lens. Modern lenses are made of many groups of glass, and these groups can be arranged so that the optical distance seems longer or shorter than the lens body. The body of a 200-millimeter lens can be shorter than twenty centimeters. You need to read the number not as a length measured with a ruler, but as a value that describes how the lens magnifies light.

How is the angle of view decided?

As focal length gets shorter, the lens fits a wider part of the scene onto the sensor; as it gets longer, it shows a narrower part, magnified. This width is called the angle of view. The angle of view is decided by focal length together with the size of the sensor; it is usually measured along the sensor diagonal, that is, the line stretching from one corner of the sensor to the opposite corner.

On the sensor called full frame, the diagonal is about 43 millimeters. On this sensor a 24-millimeter lens sees an angle of about 84 degrees along the diagonal; 50 millimeters about 47 degrees, and 200 millimeters only around 12 degrees. When the same lens is put on a smaller sensor, the sensor catches only the middle of the image and the angle of view narrows; the crop factor in Lesson 10.8 is the measure of this narrowing. That is why, when saying how wide a lens sees, you also need to know which sensor it is used on.

How does focal length change magnification?

When shooting from the same place, when focal length doubles, the subject appears twice as big in the frame. When you switch from 50 millimeters to 100 millimeters, the fisher's face grows twice as big; when you switch to 200 millimeters, it grows four times compared with 50 millimeters. This magnification has a flip side: the area entering the frame shrinks by its square, so at four times magnification only a sixteenth of the scene fits into the frame.

Two numbers are written on a zoom lens, such as 24–70 or 70–200. These numbers show the zoom range the lens covers, that is, the two ends the lens can go down to and up to. When you turn the zoom ring, you choose the focal length you want within this range without moving the camera. A phone's main camera, too, usually gives the angle of a lens of about 24 to 26 millimeters on a full-frame camera; the phone's 2x or 3x camera corresponds to two or three times this number.

What doesn't change when you shoot from the same place?

If you stand at one spot and crop the middle of the frame you took at 24 millimeters, you get an image very similar to the frame you took from the same place at 50 millimeters; it just has less detail. This shows something important: when shooting from the same place, focal length changes only how much of the frame you see. The size of objects relative to each other, that is how big the boat in front looks compared with the lighthouse behind, depends on where you stand.

This knowledge is especially important in portraits. A face's proportions, how big the nose looks compared with the ears, are decided not by focal length but by your distance from the face. When you need to come very close to fit the face into the frame with a wide angle, the face changes shape; a long focal length, on the other hand, lets you build the same frame from farther away and leaves the face's proportions more familiar. This rule works the same on a dark-skinned face as on a freckled face; what changes is only where you need to stand.

Visual evidence

You go back to the pier. In the 24-millimeter frame there is the whole curve of the harbor, rows of boats, the lighthouse and the gulls above it; the fisher on the boat is a small figure on the deck. When you switch to 50 millimeters, the lighthouse leaves the frame; the boat fills the frame and the fisher can be seen gathering the net. The coils of rope on the deck, the gunwale with its peeling paint and the boat's name can now be read; but the fisher's face is still small, and the expression can't be made out.

At 200 millimeters only the young fisher is left in the frame: a light-skinned, freckled face slightly reddened in the sun, salt grains in a red beard, cut marks on the fingers holding the net's wet ropes. You never came closer to the fisher; the face's proportions, the nose and ears, are as they are. So that the face doesn't slip into white in the very bright sun, you stop the exposure down a little for the face. The same pier, the same place; what changed was only how wide or narrow the lens saw.

Common mistakes

Summary

Focal length is the optical distance at which a lens gathers the rays coming from infinity onto the sensor, and it is written in millimeters; it isn't the lens's physical length. Together with sensor size it decides the angle of view: on a full-frame sensor 24 millimeters sees about 84, 50 millimeters about 47, 200 millimeters about 12 degrees. Doubling focal length from the same place makes the subject twice as big, but the proportions of objects relative to each other and the shape of a face are decided, on every skin, not by focal length but by where you stand.

Mini assignment

In this assignment you will shoot from the same place with different focal lengths and compare angle of view and magnification.

1. Stand at one spot and photograph the same scene with the widest, middle and narrowest angle of the lens or phone you have.
2. Crop the frame you took at the shortest focal length so that it matches the frame at the longest focal length, and compare the two frames.
3. Measure how many times an object, for example a door knocker, grows between two different focal lengths, and compare it with the ratio of the focal lengths.
4. Photograph a friend's face first very close with a wide angle, then from far away with a long focal length at the same size, and compare the face's proportions.

Check yourself

• Does the cropped wide-angle frame look like the frame you took from the same place with the long focal length?
• Did the object's growth ratio come out close to the ratio of the focal lengths?
• In the two portraits you took from close and from far, regardless of skin tone, are the face's proportions different?

Glossary

Mini quiz

1. On a full-frame sensor, about how many degrees does a 50-millimeter lens see along the diagonal?

• A) About 12 degrees
• B) About 47 degrees
• C) About 84 degrees
• D) About 180 degrees

2. When switching from 50 millimeters to 200 millimeters from the same place, how many times bigger does the subject get in the frame?

• A) Two times
• B) Sixteen times
• C) Four times
• D) It doesn't get bigger

3. How does the angle of view change when the same lens is put on a smaller sensor?

• A) It widens
• B) It doesn't change
• C) The lens doesn't work
• D) It narrows

4. What really decides a face's proportions in a portrait?

• A) The camera's distance from the face
• B) Only focal length
• C) The skin's tone
• D) The lens's physical length

Answers

1. B — On the full-frame sensor's diagonal of about 43 millimeters, 50 millimeters sees an angle of about 47 degrees.
2. C — From the same place, magnification is in direct proportion to focal length; 200 is four times 50.
3. D — A small sensor catches only the middle of the image; it sees narrower by the crop factor.
4. A — How big the nose looks compared with the ears changes with distance from the face; focal length only decides how much area from that distance enters the frame.

Summary card

• Focal length is an optical distance; it isn't the lens's length.
• A short focal length sees wide, a long one narrow: on full frame 24 mm ~84°, 50 mm ~47°, 200 mm ~12°.
• From the same place, double focal length → subject twice as big.
• Angle of view depends on sensor size too.
• On every skin, distance decides a face's proportions; focal length changes where you stand.

Bridge to the next lesson

On the pier you changed lenses without moving at all, and only the width of the frame changed. But when photographers change lenses, they often change their place too: with a wide angle they get right up to the subject, with a long lens they stay far away. Then what the photo tells changes too. Why does a wide angle make everything look big, and why does a telephoto read like a selective gaze? The next lesson talks about wide, normal and telephoto lenses, and the view each one adds to a photo.