Lenses: focal length, angle of view and framing

Learn to estimate the framing that you will obtain with a certain objective (field of view) at a certain distance from the scene.

As we saw in the article on the focal length of the lenses , in photography the focal length is basically a synonym for the angle of view .

The angle of view depends on the focal length of the objective and the size of the surface where the image is projected (photographic film or sensor)

For historical reasons, 35mm film is used as a reference (which corresponds to Full Frame sensors in digital cameras)

What is the angle of view?

It is the angle, the portion of the scene, that we can frame in our sensor (or film) using a lens with a certain focal length.

Basic rules:

  • Distances short focal : viewing angle very wide
  • Distances focal lengths : viewing angle very narrow
  • Large pickup surface (large sensor ) – increased viewing angle
  • Small surface area (small sensor ): lower angle of view (crop)

Angle of view vs Focal length

As we have commented, in photography the 35mm film or the Full Frame sensor (36 × 24 mm) is taken as reference

Knowing the focal length and the size of the sensor, the angle of view can be calculated by trigonometry … but I have never seen a photographer with a calculator in hand to know the exact angle that he will achieve with his equipment.

The angle of view is something that is internalized.

Intuitively, with experience, you get an idea of ​​the type of framing that each lens will give you (its focal length) in certain situations.

  • The angular and wide angle you get a wide viewing angle .
  • Medium focal length lenses (normal) give an angle of view that closely resembles the perception we have when looking at that scene with our own eyes.
  • Long-focal lenses ( telephoto lenses ) give us an increasingly narrow angle, which we often associate with the ‘reach’ of that lens to photograph distant objects.

Equivalent angle of view and focal length

The angle of view depends on the size of the sensor .

If we had to take into account all sizes of sensor and film we would go crazy with the viewing angles.

In photography it is spoken in the language of 35mm film.

All photographers know how a certain focal length would behave (approximately what angle of view it would have) in a 35mm frame or a Full Frame sensor.

So that we all speak in that language, what you do is ‘ transform ‘ the focal length of the lens, normalize it based on the size of the sensor.

The crop factor and equivalent focal length appear here .

For example, imagine we have a camera with a Full Frame sensor and a camera with an APS-C sensor, and a single 50mm lens compatible with both cameras.

A typical APS-C sensor applies a 1.5x crop factor (it’s its size ratio to a Full Frame sensor)

When we place the 50mm lens on the APS-C camera, the angle of view that we obtain in the photo is similar to that which we would obtain in the Full Frame camera with a 75mm lens (1.5 x 50 = 75).

So we say that this lens (in our camera) has an equivalent focal length of 75mm

The focal length is an optical characteristic of the lens , it does not change. The lens will have the same optical characteristics in any camera or in whatever use we give it.

The equivalent focal length is simply a gimmick, a normalization, which allows us to intuitively estimate from the head, what kind of frames we are going to achieve with that lens in that camera.

Here’s an example of viewing angles on cameras with APS-C sensor for lenses of different focal lengths. In black is the real focal length of the lens and in parentheses the equivalent focal length in that particular camera.

What is the field of view?

The field of view tells us how much of a scene fits within the frame (occupies the entire frame) for a given focal length (and camera).

It is measured in units of length, in meters for example.

 

How is field of view related to angle of view?

The field of view depends on the angle of view and the distance between the camera and the scene .

We are going to see it with an example.

Let’s assume a certain equivalent focal length: 400mm

Now we find ourselves a good friend (one of those who have a lot of patience) and we tell him to place himself at a certain distance from our camera: first at 25m, then at 50m … and so on.

Our equipment has the same angle of view , which corresponds to the equivalent focal length of 400m.

However, the field of view in each photo is different .

At 25m the field of view is about 2m (horizontal) and our friend looks very large in the frame.

At 400m the field of view is about 35m wide and comparatively the person looks much smaller.

If we now test with a 200mm lens, the angle of view will change (now it will be wider).

Comparatively, placing the person at the same distances, the field of view will also be wider with respect to the 400mm lens.

Then below we will see how to estimate the field of view and what use it could be.

So, summarizing:

  • Viewing angle (in English Angle of View – AOV ) refers to the angle that covers our combination of lens and camera. It is measured in degrees
  • FOV (Field of View English – FOV ) refers to the actual size of the scene that fits within our framework. It is measured in meters

In practice everyone swaps names and you will find the term FOV much more to actually refer to the angle of view.

So when you hear and read FOV they are almost certainly referring to an angle.

Why do we want to know the field of view?

In general, it is rare that we need to know the field of vision for typical day-to-day situations, especially in photography.

When could we be interested?

  • When we are going to buy a new lens and we are evaluating which focal length interests us the most
  • When we are planning a photographic outing and we want to know what equipment we are interested in bringing and what frames we will have from different locations
  • In professional film and video productions all scenes need to be planned very well. In many cases it is very important to know in detail the field of view of each shot. For example, imagine that you have a set for a scene, or you are looking for a very specific frame that includes several elements, etc.

 

Below we see some real examples so that you can get an idea of ​​use.

How to estimate the field of view

This calculation is only valid for straight lenses, it would not be valid for fisheye lenses.

And it is only valid when the subject is at a certain distance from the camera, such that that distance is considerably greater than the focal length of the lens itself.

Steps we are going to follow:

1.- What is the equivalent focal length of the lens in our camera?

For example, if we used a 50mm on a camera with a Nikon APS-C sensor, the equivalent focal length would be 75mm.

2.- What angle of view corresponds to that equivalent focal length?

From the angle of view we would have to calculate the tangent (of the half of said angle). But we have it already calculated in this table:

The multiplication factor that appears in the table is the result of this formula: 2 * tan (ang / 2)

The displayed angle corresponds to the horizontal viewing angle .

For the example that we are following, the equivalent focal length of 75mm corresponds to a factor of 0.5

3.- We estimate the distance to the subject

The more precise the distance from which we are going to use the camera, the better. In many cases it would be worth a rough estimate.

Imagine, for example, that we are going to stand 5 meters from the person to take a portrait.

4.- We calculate the field of vision at that distance

We simply multiply the factor by the distance.

In the example: 5m x 0.5 = 2.5m

The horizontal field of view of the scene would be 2.5m wide. Since the sensor has a 3: 2 form factor, the height of the vertical field of view would be approximately 1.7m

Example 1 – Telephoto lens for bird photography

Imagine we are looking for a telephoto lens for bird photography .

Let’s suppose we want to photograph the lesser kestrel , which is about 35cm long. And we want to have an idea of ​​the type of framing that we are going to achieve with different focal lengths depending on the distance at which we can approach.

We have a Canon APS-C camera: 1.6x crop factor

Let’s see first with a 300mm telephoto lens

1.- Equivalent focal length: 1.6 x 300 = 480mm

2.- We do not have the exact focal length in the table, but we can estimate that the factor would be an intermediate value, for example 0.08

3.- We are going to observe the lesser from the ground and the bird will be in a tower about 30 meters high. We will also estimate 100 meters for when we try to track in flight.

4.- We calculate:

30m -> 0.08 * 30 = 2.4 meters wide

Approximate field of view height: 2.4 * 2/3 = 1.6 meters high (160cm)

The lesser (about 35cm) would cover about 1/4 of our frame .

Would not be bad.

For in-flight photography:

100m -> 0.08 * 100 = 8 meters wide

Assuming a wing span of about 70 cm (0.7 m), this time horizontal, the lesser would cover about 9% of our frame .

How about a 400mm?

The equivalent focal length in our camera would be 640mm

The multiplication factor would be 0.06

30m -> 0.06 * 30 = 1.8 meters wide

Frame height (since we are going to photograph it posed, vertically): 1.8 * 2/3 = 1.2 meters (120cm)

The lesser would occupy approximately 30% of the frame .

Photography in flight:

100m -> 0.06 * 100 = 6 meters (horizontal width of our field of view at that distance)

The lesser would occupy approximately 12% of our horizontal frame.

Example 2 – Home recording studio for youtube

We want to set up a small recording studio for YouTube in one of the rooms of our house.

We are looking for a fixed lens to improve the quality of our videos, for shots in which we appear in front of the camera talking.

The room is relatively small, so we want to know if we would be more interested in a 50mm or a 35mm

The room is about 5 meters long, but we have to leave a margin with the back wall and also a small margin for the camera on the tripod.

The actual distance between the camera and the person will be about 3

Our camera is a Sony with APS-C sensor: 1.5x crop factor

Let’s go there with the 50mm :

  • Equivalent Focal: 50 * 1.5 = 75mm
  • Multiplication factor: 0.5
  • Distance: 3.5m
  • Horizontal field of view: 3.5 * 0.5 = 1.75 meters
  • Vertical field of view: 1.75 * 2/3 = 1.16 meters

It would be good for a medium shot: from the head, with a little air above, to the hips. Perfect for shots in which we appear seated.

We now see with the 35mm :

  • Equivalent Focal: 35 * 1.5 = 52.5mm (approx. 50mm)
  • Multiplication factor: 0.7
  • Distance: 3.5m
  • Horizontal field of view: 3.5 * 0.7 = 2.45 meters
  • Vertical field of view: 2.45 * 2/3 = 1.63 meters

It would be very fair for full body shots depending on our height. We would have to assess whether we are interested in having that extra margin that the 35mm provides us (giving up a little perhaps part of the background blur) or if we prefer the 50mm although it limits us a bit the type of shots that we are going to do in that study.

Example 3 – Planning photographic outings

The idea here is the following:

We want to take a series of photos in a natural environment and we are going to look for very specific frames for our composition.

Imagine, for example, that you want to take several characteristic elements of the area in the same frame.

You have to plan from which points you can take the photo (viewpoints, trails, etc.), at what distances the elements of the landscape will be with respect to your camera and the distances between them, to get an idea of ​​the frames and focal points you would need .

This planning is more complex, or more than complex it would be a bit tedious to do it by hand.

You can use Google Maps, with its utility of measuring distances, which will give you a pretty good approximation.

Normally you want to estimate what angle you would need to cover a landscape (minimum focal length) with all those elements from your observation point.

Or also, if you are looking for detail photography (a distant landmark for example) to get an idea of ​​how that element would appear in your frame with the focal length you are going to use .

For example, if your maximum focal length is 200mm, what frame can you get from point A and from point B, to get the maximum detail of that landmark you want to photograph.

In practice, there are mobile applications such as PhotoPills that allow you to plan your outings in great detail, including the trajectories of the sun and the moon, the Milky Way, etc. for the location where you are going to be, schedules …

And their tools also include field of view estimators .