The focal length is one of the characteristics that define the behavior of a camera lens. It influences the appearance of the photographs and the sensations they convey
All of us who start in the world of SLRs, of photography in general, feel entirely lost with some terms and concepts.
Suppose you have used compact cameras or a mobile camera. In that case, the typical situation is when you have been talking about zoom all your life, and suddenly the people of the reflex planet start talking about focal lengths … and you ask, but how much zoom is that?
It has happened to me, and it has happened to many of us. It seems too complicated a subject with physical and mathematical concepts, but the trick is easier than it looks when it is caught.
Focal length in photography
The focal length is an optical characteristic of lenses and mirrors.
In a converging lens (like a magnifying glass), the rays of light parallel to the axis that passes through it converge at a point called the focus.
The focal length is the distance between the optical center of the lens and the focal point (focus)
In a camera, the objective as a whole behaves like a converging lens (although internally, it is made up of several lenses of different types) and projects an inverted image onto the image plane, where the camera sensor is located.
Imagine that you have a hollow tube, a cardboard tube, for example, with a specific diameter and a certain length.
If you look through a long, narrow tube, you will have a narrow-angle of view. Looking through a short, wide tube will give you a wider angle of view.
Something similar happens with the objectives:
- Lenses with long focal length will project only a small part of the scene, which corresponds to an angle of vision closed.
- Lenses with a short focal length will launch a wider part of the stage, thus offering a greater angle of view. In photography, the focal length is a synonym for an angle of view.
We can also refer to the focal length as ‘focal’: this lens has a 35mm focal length, this lens has a variable focal length …
In general, when we talk about focal length, we refer to what angle of view a particular objective will provide us in a specific camera.
Why don’t we talk about angles (degrees) instead of focal length (millimeters)?
Well, there are several reasons.
First of all, the focal length is a physical property of the lens, which does not depend on anything else.
While the angle of view depends on external factors such as the physical dimensions of the lens and the projection surface (the sensor in this case)
Second, historically, since the beginning of the 20th century, 35mm film became a standard that has continued to be used until the advent of digital cameras.
As all cameras used the same projection surface, there was no need to think about viewing angles; the photographer knew from experience that a specific focal length (focal length) would provide a certain angle of view.
Things got a bit complicated with the advent of digital cameras since cameras use sensors of different sizes (different projection surfaces).
Each camera will have a different angle of view for the same focal length depending on its sensor’s size.
To normalize or get an idea of the angle of view that a lens will have (focal length) in an individual camera, the multiplication factor or crop factor is used.
Using the crop factor, you can mentally calculate the equivalent focal length of that lens on that camera in terms of its angle of view, taking as reference the 35mm film or the Full Frame sensor (approximately 35mm)
So what effects does the focal length of a lens have on the image of a scene:
- The focal length determines the angle of view. Long focal lengths (telephoto lenses) equate to a small angle of view, just a tiny portion of the scene. Short focal lengths (wide) equate to a large viewing angle, a large amount of the stage.
- The focal length determines the feeling of ‘reach’ of the lens. Telephoto lenses give the sensation of enlarging objects far away, of zooming in on distant scenes.
- Angular lenses, by a perspective effect, highlight or magnify the closest objects concerning the farthest ones. That is, they separate the planes a lot (near, medium, far). Things close to the camera appear much more extensive, and objects far away appear much smaller and much further apart.
- Telephoto lenses tend to have the opposite effect: they compress the shots so that things that are physically far apart (concerning the camera) will appear in the image giving the impression of being closer together. Here we explain in more detail what plane compression depends on.
- Focal length also affects depth of field (the part of the scene that is in focus)
Understanding the focal length in lenses and objectives
The focal length is a concept that has to do with the behavior of lenses and mirrors.
A physical effect known as light refraction occurs in the lenses: light rays change direction when passing from one medium to another (air-glass-air).
In a typical converging lens (imagine a magnifying glass), the geometric construction causes the rays to be directed towards the symmetry axis.
There is a particular point on that axis of symmetry, where all the rays that come parallel to the axis are concentrated. That point is called the focus, and the distance between the center of the lens and that focus is called the focal length.
The best way to imagine it is to think of the magnifying glass when we put it in the sun on a surface. The spotlight is the point that concentrates all the sunlight (and all the energy in that super bright spot). To achieve this point, we will have to separate the magnifying glass from the surface gradually. Depending on the lens’s shape, we will have to separate the magnifying glass from the body. That separation is the focal distance (because the rays we are using as a reference come parallel to the lens’s symmetry axis since they come from an object located far away).
Rules for Ray Tracing on an Ideal Thin Converging Lens
Here in the image, we see represented different rules or laws that light rays comply with when passing through a converging lens:
All the rays that leave from an object’s point will converge in a single moment when passing through the lens. At that point, the beams ‘add their information,’ and the image appears sharp.
The lens formula gives us the relationship between:
The distance between the object and the lens (c)
The focal length (f), which is a characteristic of the lens
Space at which the image of the object is formed (di), which depends on the focal length and the distance at which the object is
Planes instead of points
As images are usually projected on flat surfaces (e.g., imagine a movie being projected on a cinema screen), we speak of planes instead of points.
We then have:
- The plane of the object (all points on the object that are the same distance from the lens)
- The focal plane (located right in focus)
- The image plane (projection that corresponds to the image of the object plane)
For each real scene, there are infinite possible image planes.
We are interested in the image plane that corresponds to the projection of the object of interest. The shots in front and behind do not interest us (they will appear out of focus).
Therefore, we place the sensor just at a distance (di) so that the image plane (of that particular object) coincides with the sensor plane.
In a camera, we do not move the sensor back and forth to put it in the image plane that interests us. We carry the lens (actually the focus lens) or move the camera directly, usually done in photography macro.
Image and focus planes
When there are several objects in a scene located at different distances from the camera, only one will appear correctly in focus.
Each object is projected through the lens onto a different image plane.
We will place the sensor just at the distance that corresponds to the object of interest’s image plane.
For other objects (for example, an item located further away from the camera), its rays will be converging in a different image plane, which will not coincide with the sensor plane.
These rays are projected onto the sensor but do not add information but instead mix and give rise to diffuse (out of focus) images.
Logically there is a range of distances within which all objects ‘appear’ in focus and sharp. This has to do with other factors, such as human visual perception and depth of field.
You can also see how the focus system of the cameras works.
Objectives (optical systems)
In a real camera lens, there is no single lens. The objectives are made up of several lenses to achieve specific optical characteristics and correct individual natural physical lens defects.
But the behavior of this entire lens system can be associated with a single ideal lens located in the optical center of the objective.
Therefore the focal length of a lens would be the distance between that optical center and the focus.
The optical center may be outside the lens itself.
For example, imagine a lens with a 600mm focal length.
The lens itself (physically) is not 600mm long. It is much smaller. But the combination of lenses inside makes it behave like an ideal lens with a 600mm focal length.
The optical center of that lens would be outside the lens itself, well ahead of the front lens.
Confusion about the different planes
When you read about these topics, there is often a tremendous confusion of terms, especially between the focal plane, the sensor plane, and the image plane.
As a summary, so that there are no doubts, we are going to list the different planes involved:
- Object plane
All points of the object of interest in the scene, located approximately the same distance from the camera
- Focal plane (focal length)
It is a characteristic of the lens, and it has nothing to do with the camera.
plane It is the place where the points of the object of interest are projected, where all the rays ‘add up’ and generate a sharp image
- Sensor plane
It is a characteristic of the camera. It has nothing to do with the focal plane (objective). The sensor’s position (and therefore the sensor plane) is indicated in many cameras by a circle crossed by a line. The line shows the part of the front of the sensor.
Logically everything has to be calculated so that the image plane coincides with the sensor plane, at least for the objects (distances) that we usually photograph. If not, we would have a problem.🙂
Why is there so much confusion?
First, the sensor plane and the image plane coincide for the object of interest (the thing we want to show in focus).
Second, because the terminology: ‘focus’ or ‘put in focus,’ ‘out of focus, etc … refers to the lens’s focus and implies that it is the image that is in focus.’
Third because in a camera, for the most common situations, the distances between the focus (focal plane) and the sensor (image plane for a particular object) are minimal.
This is because the object’s distance is usually on meters, while the focal length is on millimeters.
If you do the math with the formula for thin converging lenses (ideal), you will see that the difference in distances between the focus (f) and the image plane (di) is minimal.
Let’s do a practical example with an object located at 5 meters and a 50mm lens (50mm focal length = 0.05m):
(1/5) + (1 / di) = (1 / 0.05)
di = 0.0505 = 50.5 mm
The focal plane is 50mm from the optical center, and the image plane for that object is formed 0.5mm from the focal plane.
For an object located very far away, for example 100 meters :
(1/100) + (1 / di) = (1 / 0.05)
di = 0.050025 = 50.025 mm
The image plane is only 0.025mm from the focal plane.
Now an object located 50cm with the same 50mm objective :
(1 / 0.5) + (1 / di) = (1 / 0.05)
di = 0.0556 = 55.6 mm
The image plane is formed 5.6 mm from the focal plane.
When the plans do not match
Can it happen that the sensor plane does not coincide with the image plane?
The camera + lens system has to be designed to be projected onto the sensor. But this only happens for a range of distances.
Typically all lenses are calibrated to focus at infinity (objects that are very far away).
But on the other hand, each lens has a minimum focus distance.
If we bring the camera closer to the object below that distance, we will not focus: the image plane will be behind the sensor, and there will be no way to get it focused.
Macro lenses allow their optical center to be widely separated (relative to the sensor plane). In this way, we can get the camera closer to the object.
If you use extension tubes with a lens, you will separate its optical center concerning the sensor’s plane, and you can bring the camera closer. But in that case, you will surely lose focus at the infinity of the lens.
As you can see, depending on the characteristics of the lens and the camera, we will have an operating range. A range of distances for which we can use the objective.
Fixed focal length and variable focal length lenses
As we have discussed, photographic lenses are made up of many lenses. But the set behaves like a single ‘ideal’ lens, and one of its main properties is its focal length.
Some lenses have a specific focal length: fixed focal length, set, prime (in English)
And there are lenses that, by internally shifting their lens configuration, allow you to adjust to a range of focal lengths: they are variable focal lenses, also known as zoom lenses.
The focal length of the lenses is measured in millimeters; with variable focal lenses, the range of focal lengths is always indicated.
For example, 18-55mm would indicate that the lens can go from a focal length of 18mm to a focal length of 55mm, including all focal lengths in between.
Focal length and angle of view
Another way to think about focal length is by relating it to an angle of view.
Historically, as we discussed at the beginning, 35mm film has always been used as a reference.
Therefore, everything discussed in this section regarding viewing angles is valid only for cameras with a
Full Frame sensor (35mm).
A medium focal length would correspond to the human eye’s angle of view, about 45 degrees (not counting peripheral vision). The equivalent would be a 50mm lens.
A small focal length equates to a larger angle of view. Lenses with a short focal length are called wide-angle and wide-angle lenses (35mm and below). 15mm lenses are called fisheye and have a 180º angle of view.
A long focal length equates to a narrower angle of view. Lenses with focal lengths above 70-80mm are considered telephoto lenses, and their angle of view is less than 30º. As if of the entire possible scene, we focus only on a much smaller area, which occupies the whole frame ( we enlarge it ).
Focal length and sensor size. Clipping factor
The relationship of the focal length to the effective angle of view is not fixed. Current lenses have evolved from analog cameras with 35mm film, corresponding to Full Frame sensors.
If we use a lens with a Full Frame camera, the effective angle of view will be similar to that of an analog SLR camera.
If we use that same lens with a camera with a smaller sensor, the result is that we only take advantage of a smaller part of the same scene (concerning a full-frame sensor, it is as if we cut out the central region and discarded the rest ). If we think of viewing angle, it is equivalent to reducing the tip, and if we think of magnification, it is equal to enlarging the scene.
Therefore, smaller sensors introduce a crop factor into the image, translating into a multiplying factor for the focal length for practical purposes. The shorter the sensor is relative to a Full Frame, the greater the lens’s sufficient focal length.
If to frame an object with a full-frame, you have to place yourself at a certain distance, using the same lens with a camera with an APS-C sensor. You will have to identify yourself at a greater distance to achieve the same frame. If the sensor were smaller, the further you would have to position yourself from the object.
Or if you want to see it in another way: if we place two cameras (one Full Frame and the other APS-C) at the same distance from the scene, the two cameras with a lens of the same focal length, the resulting photo from the APS camera -C will show an ‘enlargement’ of the scene concerning Full Frame, by a factor equivalent to the difference in the size of the sensors.
Cameras with APS-C sensors have a crop factor of 1.5 – 1.6 (depends on the sensor’s exact size).
When it comes to the angle of view, the photographer’s actual focal length is not the lens’s exact focal length but the sufficient focal length or equivalent of that lens on his camera.
For example, a 50mm lens mounted on an APS-C camera is for practical purposes equivalent to a 75mm (50 x 1.5 = 75), practically a telephoto lens, with an angle of view of around 35º instead of the 45º that 50mm would have on a camera with a Full Frame sensor.
We always talk about the equivalent focal length or sufficient focal length to reference and compare because the focal length of a lens is what it is. It is a characteristic of the lens, regardless of where it is mounted or used.
This would be a comparison table for an APS-C sensor camera. In black is the real focal length of the lens (for which it has been manufactured) and in blue is the approximate sufficient focal length.
An APS-C camera with a 35mm lens would take a very similar photo (in terms of angle of view) to a Full
Frame camera with a 50mm lens.
We usually look for the greatest possible focal length (greater magnification of distant objects). Therefore the multiplicative factor of the APS-C sensor plays in this case favor. For example, a 70-300mm lens mounted on an APS-C will behave like 100-450mm.
For angular lenses, the opposite is true. The crop factor causes the angles to lose angle of view when used in cameras with a smaller sensor.
Plane, perspective, and focal length compression
In photography and video, what we do is represent a real scene on a 2-dimensional plane. The representation of three-dimensional scenes in a flat image is called perspective. The word perspective is also often associated or used as a synonym for ‘ point of view. ‘
The perspective gives us only partial information about the scene (since we have lost one of the dimensions). When we see an image, the brain interprets the perspective and builds a representation in its way of the real scene, the distance between elements, depth, etc.
The plane compression often associated with telephoto lenses and the geometric distortion usually associated with wide-angle lenses are perspective effects.
Any lens, whatever its focal length, will compress the planes or exaggerate their separation depending on how far the scene’s objects are from the camera.
Plane compression does not depend on the focal length, only on the camera’s distance and the scene elements.
It is a question of geometry; you don’t need a camera to check it. You can check it with paper and a pencil.
Imagine a scene with a central element (the protagonist) and a series of secondary pieces placed in the background at some distance.
We will project these elements onto a plane, using image construction rules similar to those of any camera. The only difference is that in this example, for simplicity, we are going to imagine that the canvas is in front of our eyes (as we look towards the scene). In contrast, in a camera, the ‘canvas’ would be the sensor and be on the other side of the objective’s focus.
As you can see, we do not change the image plane’s size or the angle of view. The only thing we change is the distance between the image plane and the scene.
Each of the projections A, B, and C would correspond to three different images that we would obtain with our camera, using in all three cases the same objective (with the same focal length)
And if you look closely, each of those images has a different perspective; that is, it makes a diverse representation of the same three-dimensional scene.
When we get very close to the elements of the scene, the perspective exaggerates the proportions and the sensation of depth (separation between the main object and the background)
When we zoom out too far, the perspective has the opposite effect: the proportions equalize, and the feeling is that the scene has much less depth. This effect is known as plane compression.
In practice, what we want is a specific frame and a particular style or effect.
For example, if we want a closed frame for a portrait (half body, only face …) and we use an angle lens, we know that the face will be distorted (large nose, small ears …)
In the case of telephoto lenses, we usually use them to photograph distant elements. These elements, together with the background and the intermediate parts of the scene, will appear with less depth and with sizes (plane compression)
In practice, although these effects are related to perspective, for most situations, it can be assumed that angular lenses provide that feeling of depth, separation of planes. In contrast, telephoto lenses give that feeling of plane compression.
What does focal length have to do with the ‘zoom’ label that appears on some cameras? And with the magnification of binoculars?
First of all, it must be said that zoom is the process of zooming in or out (zooming in), the action of changing the focal length of a lens. It does not indicate how much ‘rise’ or how far a goal is to reach.
Talking about zoom only makes sense on variable focal lenses.
Compact and compact superzoom cameras typically display range, the ratio of the most extended focal length the lens offers to the shortest. It is merely a marketing tag.
For example, in a compact with a 24x zoom, this value indicates that the most extended focal length is 24 times the shortest focal length. So if the smallest focal length is 25mm, the most extended focal length would be: 25 x 24 = 600mm.
The compact cameras with small sensors usually indicate equivalent focal lengths. The crop factor is applied to easily compare against the targets SLR camera, always referenced to the film or sensor 35mm. But the actual focal lengths of its lenses are much shorter. For the example we have seen previously (25-625mm), it is a real camera with a 5.55 crop factor so that the actual focal lengths would be: 4.5-108mm.
As you can see, the zoom value does not tell us much; it only gives us a little idea that this lens covers a more or less sizeable focal range. In general, zoom values (x10, x20…) are only used in compact cameras.
The lenses of reflex and mirrorless cameras indicate the actual focal length (the minimum and maximum in variable focal lenses). Examples:
In binoculars, it is different. ‘magnifications characterize binoculars.’ For example, ten × 50 binoculars (or only 10x, since the second value is the aperture) have a magnification capacity of 10. That is, they magnify a distant object ten times concerning its size with the naked eye.
The operation of binoculars is somewhat different from cameras since they have two main optical groups: the one that would correspond to a camera’s objective and the one that constitutes the eyepiece.
There is no direct relationship between the magnification of binoculars and the focal length of a camera lens.
A thumb rule takes the 50mm lens (on 35mm film or sensor) as a reference and matches it to 1x. So a 10x would roughly correspond to a 500mm. But it is only an approximation.