How does the focal length change perspective?

Suppose you are 10 feet from your friend Joe and take his portrait orientation photo with a 50mm lens. Let's say there is a building 100 feet behind Joe. The building is 10 times farther from the camera than Joe, so if Joe is 6 feet and the building is 60 feet, they will appear to be the same height in your photo, as the two would occupy approximately 33º of the image. 39º angle of view of a 50mm lens on the longest dimension.

Now save 30 feet and use a 200mm lens. Your total distance from Joe is now 40 feet. Since you are using a focal length 4 times greater than the original 50 mm (50 mm X 4 = 200 mm), it will appear on the second photo at the same height as on the first. The building, however, is now 130 feet from the camera. It's only 1.3 times higher than when you first shot (100 feet X 1.3 = 130 feet), but you've increased the focal length by 4 times. Now the 60 foot tall building will appear to be about 3X the height of Joe in the image (100 feet / 130 feet = 0.77; 0.77 X 4 = 3.08). At least, that would be the case if all of this could get into the picture, but that is not the case.

Another way of looking at it is that in the first photo with the 50mm lens, the building was 10X further away than Joe (100 feet / 10 feet = 10). In the second photo with the 200mm objective, the building was only 3.25 times further away than Joe (130 feet / 40 feet = 3.25), even if the distance between Joe and the building was the same. What has changed is the relationship between the distance between the camera and Joe and the distance between the camera and the building. This is what defines the perspective: The ratio of the distances between the camera and various elements of a scene.

relationship between focal length, perspective projection and camera distance

One thing and only one thing determines perspective: the distance from the subject. Period.

For more information, please see:
Is there a difference between a distant shot on a 50mm lens and a close-up shot on a 35mm lens?
Is the wide angle equivalent in the image of the crop sensor?
Can a telephoto lens have a wide field of vision?
How does the focal length change perspective?
Why is the background bigger and more blurry in one of these images?
What does it really mean that telephoto lenses "flatten" the scenes?

I think your fundamental confusion expressed in the question is due to the different ways in which the different sources you are looking at use the word perspective. They don't all mean the same thing when they use the same word.

The term perspective projection does not describe the same thing as "the perspective of the image". The term geometric projection, in my opinion, is a more precise way of saying what is meant by perspective projection. In other words, it describes how the lens projects an image of the 3D world onto a 2D medium such as a film or a sensor.

The difference is covered in more detail on this question here at Photography SE:
What is the difference between perspective distortion and barrel or pincushion distortion?

Perspective describes the distance relationships between the camera and various elements of the lens' field of vision. As long as the camera is in the same place and everything in front of the camera is in the same place, the perspective will be the same regardless of the focal length lens used. The focal length will determine the angle of view (as long as the film or the size of the sensor does not change), but this will not affect the perspective at all. If you take a picture with a very wide angle lens and crop the middle of the resulting image, it will look like a picture taken in the same place with a longer focal length lens providing a narrower field of view. your cropping. You would lose resolution by throwing away most of the pixels from the camera, but the perspective would be the same.

From the description of the (Perspective) tag here at Photography SE:

Perspective is the spatial relationship between a camera and the things the camera photographs. If two objects of the same size are in the scene and one is much closer to the camera than the other, the closest object will appear to be much larger than the distant object. If the two objects remain at the same distance from each other but the distance from the camera increases by two, then the difference in the apparent size of the two objects will decrease.

You ask:

If the change in focal length does not affect the perspective of the image, what affects the perspective distortion of the image?

The only thing that affects perspective is the shooting distance and the relative distances of various objects from the scene to the camera. To change the perspective, you have to change the relative distances between the camera and various elements of the scene. Here is an example of an answer to this question:

Suppose you are 10 feet from your friend Joe and take his portrait orientation photo with a 50mm lens. Let's say there is a building 100 feet behind Joe. The building is 10 times farther from the camera than Joe, so if Joe is 6 feet and the building is 60 feet, they will appear to be the same height in your photo, as the two would occupy approximately 33º of the image. 39º angle of view of a 50mm lens on the longest dimension.

Now save 30 feet and use a 200mm lens. Your total distance from Joe is now 40 feet. Since you are using a focal length 4 times greater than the original 50 mm (50 mm X 4 = 200 mm), it will appear on the second photo at the same height as on the first. The building, however, is now 130 feet from the camera. It's only 1.3 times higher than when you first shot (100 feet X 1.3 = 130 feet), but you've increased the focal length by 4 times. Now the 60 foot tall building will appear to be about 3X the height of Joe in the image (100 feet / 130 feet = 0.77; 0.77 X 4 = 3.08). At least, that would be the case if all of this could get into the picture, but that is not the case.

Another way of looking at it is that in the first photo with the 50mm lens, the building was 10X further away than Joe (100 feet / 10 feet = 10). In the second photo with the 200mm objective, the building was only 3.25 times further away than Joe (130 feet / 40 feet = 3.25), even if the distance between Joe and the building was the same. What has changed is the relationship between the distance between the camera and Joe and the distance between the camera and the building. This is what defines the perspective: The ratio of the distances between the camera and various elements of a scene.

On the other hand, even two lenses with the same focal length can have different geometric projections. This will affect the shapes of the elements of the image, but it will not change what the camera can and cannot see from the same shooting position. If the "A" box is in front of the "B" box and hides half of the "B" box from the camera, switching from a straight lens to a fisheye lens will not change the amount of box "B" visible by the camera. . That's what the prospect is. Different geometric projections can cause straight lines to appear curved or elements at the edge of the field of view to be "stretched", but that does not change the perspective.

In the real world, there is no lens with an infinite focal length. It is a figment of the imagination that can be used in CGI. To get an orthographic projection with a real camera, you need a telecentric lens.

To get a view where the objects at the end of a three-dimensional
the subject appears the same size as the objects on the side near the
subject we have to use a telecentric type lens which will give us a
orthographic view of our subject. One of the basic requirements
of a telecentric lens is that the lens must be at least as large
diameter as subject. This tends to make them very expensive.

terminology – How to explain the focal distance to someone who is not a photography lover?

Without going into the formulas, I think the easiest way to visually explain the focal length is to use an empty 35mm slide as a framing guide. (Note that over time, less and less people know what a 35mm film slide looks like, so the visual guide is less apt …)

First of all, you need to explain that focal length is a property of the lens. Just like a milk jug can hold 1 or 1/2 gallon or 1 liter, or a certain bottle of water can hold 1/2 liter, so any particular lens has a particular focal length. (In this analogy, zoom lenses are like collapsible water bottles, which have a certain minimum volume when folded down and a maximum volume when folded down). Just like volume is a property of this particular bottle, the focal length is therefore a property of this particular lens.

(Note: I didn't have to use a bottle volume for analogy. I could have used the height of the bottle as easily as the property. It doesn’t matter – it’s just an analogy)

Extending the analogy, it doesn't matter if the bottle is full, half full or empty – the capacity of the bottle is fixed. Just like with a lens: it doesn't matter if it's focused far or near – the focal distance of the lens is unchanged.

Related: What is the focal length and how does it affect my photos?

Now back to the cameras. Different focal lenses modify field of view when mounted on a certain camera. Conversely, when mounting different cameras (with different film or sensor sizes) on a particular lens, the field of vision is also affected.

Here is where the 35mm slide comes in when explaining to people: for a lens with a focal length ƒ (say, 50mm), if it was mounted on a film camera 35 mm (those that most people using film cameras know), then you will get the same field of vision just as you hold a 35mm film slide at a distance of ƒ (50mm, or about 2 inches, in this case) in front of your eye.

Another example: early in the evening of a full moon night, when the moon is low on the horizon and it looks impressive, if you want to capture it in full glory, imagine holding a empty 35 mm slide at arm's length (about 3 feet or or about 900 mm) to frame the moon. When framed with a slide holder at this distance, the moon will fill about 1/3 the height of the frame. So that gives you an idea of ​​the viewing angle of a 900mm lens on a 35mm film camera (or a 35mm full frame DSLR).

Related: What Focal Length Lens Do I Need To Photograph The Moon?


Now if you are talking about a camera with a smaller sensor, such as a 1.5 or 1.6 APS-C crop sensor on entry level DSLRs and mid-range, a 35mm film slide holder no longer works. The framing tool should be 1.5 times smaller. In this case, it would be 24 x 16 mm. Using the smaller "1.5 APS-C slider holder" as a framing guide, you can place it at the focal distance of the lens ƒ from your eye to judge the size of the field of view .

Related: Does My Crop Sensor Camera Really Turn My Lenses Into A Longer Focal Length?


This is the simplest way I have found to explain and visualize the focal distance, without delving into math with the formula of the thin lens and the formula of the angle pinhole vision.

focal length – What is the best lens choice in a surplus optics store to get a Stanhope lens type magnification function?

I'm looking to experiment with my cell phone and a lens, holding the lens in contact with the lens on my cell phone. I'm looking for a lens that has the shortest rear focal length possible, so a BFL of 0 mm being ideal. It is for the image / having in focus the surface of the lens itself, like a Stanhope lens.

If I had to choose a lens on surplusshed.com, what type of lens would bring me closest to this possibility?

I know that a spherical lens with a refractive index of 2 equals a BFL of 0, but I have found that higher refractive spherical lenses are quite expensive and overhung don't wear them.

It has been suggested to combine a rod lens with a half ball lens, but I am strictly looking for a single lens to experiment with, as I don't want to order custom lenses or cement mine because I'm a beginner.

8 – How to define the coordinates of the focal point in a view or a branch?

I am using the Focal Point module in D8, and I am trying to understand how I can access the focal point's X and Y coordinates via Twig in a Twig view or model so that I can use them as the coordinates of background position.

I can't seem to find any documentation … could someone point me in the right direction?

optical – definition of inconsistent focal length

I recently learned about cameras and I became incredibly confused as to the use of the word "focal length".

In the wiki https://en.wikipedia.org/wiki/Focal_length and other resources, it is defined as the distance between the lens and the plane where the parallel light rays converge.

This definition makes sense to me. The focal length is an intrinsic property of the lens.

But other times, I see the focal length defined as the distance between the lens and the image sensor when the subject is in focus.

But the only time these two definitions mean the same thing is if the object is far enough apart that the light rays are approximately parallel.

Then in this video (https://www.youtube.com/watch?v=xFjgQ9jutbE), the focal length is defined as the distance between the convergence of light and the image sensor.

Which one is it?

focal length – Determining the CCD width of a camera

How can I determine the CCD (width of the imaging area) based on image details such as focal length? I have pictures taken by cameras, but very little information about the cameras themselves (I have the focal length and the resolution). Given this, is there a way to determine the width of the CCD

focus – Are the internal focal focal lengths really uncompensated varifocal lenses?

If I shorten the focal length of a lens without taking further action, it will reduce the flange distance required for focusing to infinity – which means that if the actual flange distance is not changed, the focus will be closer than infinity.

Is this effect used to get an internal focus on the main lenses, and does this explain why the effective focal length decreases instead of increasing in such designs when it is focused more near?

In other words, do these lenses focus breathe BECAUSE you focus them, or do they focus breathe TO focus?

DO NOT ask questions about real cine lenses or ultra-large floating elements here.

(NB, although this may seem like a question of pure optical design not related to photography, it can become relevant when evaluating the best way to choose or modify lens adapters).

geometry – Ellipse circle of the director and diametral circle of any focal chord.

I have to prove that the diametral circle of any focal chord of an ellipse touches the director's circle: $ x ^ 2 + y ^ 2 = a ^ 2 + b ^ 2 $.

I have achieved the result using analytical geometry
But now I find a method using pure geometry and I have problems with that. I have tried to use geometric propositions of conics, but I have not reached anywhere.

focal length – What is the best choice of overhanged lens to achieve a Stanhope lens type magnification function?

I'm looking to experiment with my cell phone and a lens, holding the lens in contact with the lens on my cell phone. I'm looking for a lens that has the shortest rear focal length possible, so a BFL of 0 mm being ideal. It is for the image / having in focus the surface of the lens itself, like a Stanhope lens.

If I had to choose a lens on surplusshed.com, what type of lens would bring me the closest to this possibility?

I know that a spherical lens with a refractive index of 2 equals a BFL of 0, but I have found that spherical lenses with higher refraction are quite expensive and overhung do not wear them.

It has been suggested to combine a rod objective with a half-ball objective, but I am strictly looking for a single objective to experiment with, because I don't want to order personalized objectives or cement mine, since I am a beginner.