Understanding Perspective

Martin Bailey

Changing your subject distance and focal length affects the perspective of the visual elements in your photographs. This is often confused with a change in perspective due to your lenses focal length alone, but that really isn't the case.

The sample photos in this post were made at a park in the UK. They aren't great photos, but I wanted a scene with two distinct elements in it, one close by and one far away.

Focal Length Alone Does Not Change Perspective

This can be a confusing subject, and people often end up talking about how changing the focal length changes the perspective, but it actually does not. The only time the perspective changes is if you change the distance from your camera to the subject.

If you also change your focal length to maintain the same subject size, you will see a dramatic change in the relationship between the foreground subjects and the elements in the background. If you put a camera on a tripod without changing the distance to your subject and shoot a series of images as you zoom in or out, you can crop away the excess image that is captured in the images at wider focal lengths, and you'll see that the relationship between the main subject and the background will be exactly the same. The perspective itself does not change by changing the focal length alone.

The perspective changes in my sample photos because I moved closer to my main subject and zoomed out, therefore changing my focal length to make the main subject appear the same size in each photograph. When you do this, the relationship between the subject and the background elements changes dramatically.

The Effect of Subject Distance on Perspective

To demonstrate, I needed both a near and a distant subject so that I could explain this theory. I grew up playing in this park on holidays and weekends and knew that I'd be able to find a tree to place in front of the power station in the distance.

Image 1 (below) was made with my 24-105mm lens at 105mm from a distance of approximately 330 feet (100 meters). After making this first exposure, I made a mental note of where the tree was in the frame so that I could recreate it as I moved closer.


Image 1: Tree and power station shot at 105mm from 330 feet.

Looking at the focal length markings on the barrel of the lens, I changed from 105mm to 70mm. I walked closer to the tree, checking its size in the frame until it was approximately the same size as it was in the first photograph. Image 2 was shot at 70mm from a distance of approximately 230 feet (70 meters). Notice how the tree is the same size, but the power station behind it has shrunk slightly.

Image 2: Same subjects shot at 70mm from 230 feet.

I repeated the process, changing the focal length of my lens from 70mm to 50mm, and moved closer still to the tree, until it was the same size in the frame again and shot Image 3 approximately 180 feet (55 meters) away. Note how much smaller the power station has become.


Image 3: Shot at 50mm from 180 feet.

For Image 4, I zoomed all the way out to 24mm and moved close enough for the tree to look the same size in the frame, and shot this from approximately 82 feet (25 meters).


Image 4: Final frame, shot at 24mm from 82 feet.

When you compare all four of these images, you'll see that the tree is pretty much the same size in each, but if you look at the size of the power station in the background, you'll see that it changes dramatically as I walked closer to the tree and zoomed out to maintain the size of the tree. Why does this happen? Because it changes the field of view.

Left to right, top to bottom: the overview of all four frames.

 Field of View

By changing the focal length of your lens, you change its field of view (i.e., how much of the world you are able to capture in your image, which is directly linked to the focal length). On a full frame or 35mm sensor camera, at 105mm you can photograph horizontally 20° of the world around you. At 70mm, you get 30°, at 50mm you get 40°, and at 24mm, 75° of the scene before you enters your lens.

You can usually find the field of view for your lenses on the manufacturer's website, but I checked the field of view for each of my sample photographs with a program called <a href="https://www.rawdigger.com" target="_blank">Raw Digger</a> that allows me to dig into my EXIF data. Canon actually writes the field of view for the focal length used in the EXIF data of each image, and that's really handy.

I also went into Canon's Map Utility that comes with my GP-E2 device that I use to geotag my images and using the scale on the map and a rule against my computer display, I calculated the shooting distances that I mentioned earlier. With these two pieces of information, you can easily chart out the relationship between the four sample images, including your shooting distance and the angle of view, as you can see in the diagram below.


Calculate Subject Size Based on Distance and Degree

To really explain this, I'm going to utilize my best math skills. Believe me, I'm no mathematician; it was my worst subject at school. I hate numbers, except when it comes to something that I'm interested in, like business, computers, and photography—the only instances where I like to dig down a little. For my own sake, I wanted to make sure that I'm doing this right, and to do that, I first figured out how to calculate the size of the tree in the photograph.

Since Π (pi) = 3.14159, if you divide the widest field of view you're ever likely to use in photography—180 degrees—by 3.14159, you get 57. That means you can calculate the size of an object by multiplying the distance by the field of view in degrees and divide that by 57.

So with this formula, you can calculate that at 105mm, when I first photographed the tree from a distance of approximately 330 feet (100 meters), the field of view captured in the photograph was about 114 feet (35 meters) at the distance of the tree (100 x 20 / 57 = 114 feet).

In Adobe Illustrator, I resized the example images to 1,000 pixels wide and used the measure tool to find that tree was 440 pixels wide to determine that it takes up 44% of the field of view. So by multiplying 114 by 0.44 to learn that the tree is approximately 50 feet (15.4 meters) across at its widest point. That sounds about right!

By taking the widest focal length of 24mm and doing the calculation, you get roughly the same answer. At 24mm, the field of view is 75° and I photographed the tree from 82 feet (25 meters). So, 82 x 75 / 57 x 0.44 equals 47.24 feet (14.4 meters). There's a small variance, but I got my actual shooting distance from my GPS information, measuring it with a very small ruler on a computer screen. Something may also happen upon focusing the lens, but I'm not too concerned about this variance. It's close enough to prove to me at least, that my math isn't too cranky.

Near and Far Objects

Mathematically, you can understand why the power station gets smaller in relation to the tree by doing the same calculations. Measuring out the distance from where I was when I took these photos, I was about 11,482 feet (3,500 meters) from the power station and it takes up approximately 37% of the field of view in the 105mm focal length photograph, so, 3500 x 20 / 57 = 1228 x 0.37, the power station is about 1,490 feet (454 meters) wide from this angle.

In the 24mm photograph (Image 4), the power station takes up about 10% of the field of view, and I moved 75m closer to the subject so 3425 x 75 / 57 x 0.1, which comes to 1,476 feet (450 meters). Again, there is a slight variance, but you can see that you're able to approximately calculate the size of the objects in the frame based on the distance to the objects and the field of view of our lens at any given focal length.

Field of View in the Distance

To understand why distant objects are smaller in wider focal length images, I want to do one last pair of calculations to find the width of the slice of the world captured at the distance of the power station, kind of as a checksum. I got these numbers as part of the previous calculation, but to recap, the power station is approximately 3,500 meters away in the 105mm photo which has a field of view of 20°. At 100 meters, where the tree is, this captures 35 meters of the scene, but if we extend this out to where the power station is, we are capturing 1,228 meters of the world.

At 25 meters with a focal length of 24mm, the photo captures 108 feet (33 meters) of the world, but at 11,237 feet (3,425 meters), where the power station is, that captures a 14,764 foot- (4,500 meter) wide scene. So an object which is approximately 450mm wide is going to take up 10% of a 24mm image, as opposed to 37% of a 105mm photograph. Since I maintained the tree size at 44%, this is proof for why things get smaller as they get further away.

Not being very good at maths, after spending most of the day working on these formulas, you can imagine how happy I was to find that when I entered my calculations into an Excel spreadsheet, calculated the size of the tree and power station based on field of view and distance alone, and then calculated that the percentage of the width that the power station would take in my images was exactly the same as that which I'd calculated by measuring the pixels in Adobe Illustrator.

One Sentence Take-Away

In practical use, remember the following sentence:

"As you widen your focal length and move closer to your main subject, the background elements in your scene will appear smaller."

That's it! I know that this is somewhat obvious, and many of you will look at this sentence alone and think, "I knew that!" And that's great, but I hope now that you'll have a better understanding of why this happens. I certainly understand it better than I did when I first sat down to think about these equations.

A Practical Example

Here are additional photos from the field, not necessarily to illustrate this point, but to help get a better understanding of how different images can be just by thinking about the distance to subject and focal length.

This tree in front of a sand dune in Namibia (below) was shot from 280 feet (85 meters) from the tree (I know this because I geotag my images and checked on Google maps). My focal length for this was 80mm, but I cropped in a little along the top, so it's probably the equivalent of 90mm.


Left: Namibian dune from 280 feet. Right: From 100 feet.

The image on the right was part of a series of images that I shot vertically to stitch together as a panorama, but it didn't work because the dune looked tiny in relation to the tree.  I don't honestly know why I proceeded to shoot the series, but it helps to illustrate this point, so it's all good.

I actually shot this from around 100 feet (30 meters) away from the tree. Because I used portrait/vertical orientation with the camera for this photo, I automatically got more foreground and sky. So although it's not a straight comparison, you'll be able to appreciate how going a little bit wider and moving closer to the subject has shrunk the apparent size of the background.

Knowing that the final image is what I wanted, I exposed the next photograph (below) before the others, from around 250 feet (75 meters) away from the tree with a focal length of 165mm.

From a distance, the background looks very different in the long focal length shot when compared to the shorter focal length shot closer to the tree (even though the dune begins to rise not far from the tree). But because the sand dune is so large, it quickly recedes into the distance, quickly shrinking in relationship to this tree.


Left: From 250 feet. Right: From 4,400 feet.

I made the image on the right as we walked away from this sand dune. I shot this at a distance of 4,400 feet (1.3km) with a focal length of 200mm.

Obviously, the tree is now much smaller in the frame from this distance but think about the difference between how the tree looks in this shot compared to the first two photographs of this tree and dune above. In all three images, you can see the tree with the sand dune from top to bottom.

The apparent size of the tree in comparison to the sand dune is portrayed differently simply by changing my focal length and distance to the tree from the camera.

Don't Zoom With Your Feet Just Because

You'll often hear people talking about zooming with your feet, just as I did to get closer to the sand dune. "Zoom with your feet" is one of those mantras that people latch on to and use for a number of reasons.

I won't go into details on my theories here, but I imagine that part of the reason for the popularity of this phrase is because people need to protect their egos by justifying a decision to buy (or sometimes not to buy), a certain piece of gear. Worse yet, sometimes people are just regurgitating a phrase that someone who should know better said in a confident tone.

When photographing wild animals or a valley from a cliff edge, I prefer not to walk forward. In a situation when you can move forward, your decision to do so should be based on how the focal length (or more specifically, the field of view and the distance to your subject and scene) will affect the look of your photograph. You definitely don't want to be zooming with your feet just because someone etched that phrase into your brain.

I hope this article helps you to make an educated decision for yourself as to whether it's better to move closer to your subject or shoot it from further away while zooming with your lens, not your feet.

Want more on perspective? Listen to Martin's podcast of this very topic. 

If you like this article, learn more from Martin in his eBooks, Sharp Shooter, and Striking Landscapes.

Martin Bailey is a Tokyo-based nature and wildlife photographer and educator who is passionate about creating photographs that evoke emotions and helping others to do the same. He runs photography workshops and releases a weekly photography podcast and blog. See more of Martin's work at martinbaileyphotography.com.

Craft & Technique Martin Bailey

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Comments


  • Very cool! I know this effect in theory, but seeing it laid out this way with specific emphasis on controlling the balance of background relative to foreground is very revealing.

    David on
  • This was very helpful and makes me want to experiment on the topic. Thanks for the explanation, your good examples and last but not least – the motivation to try those tools and become creative!

    Iris on

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