Making Sense of Lens Optics for Crop Sensor Cameras

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If you have been considering getting a new camera or have been considering upgrading a camera, you have probably heard all about crop sensor cameras but what does it mean? How does crop factor affect lens selections? When you are considering systems, often it is not just the camera bodies you must consider, but the selection of lenses for that system as well.

Sensor Optics and Equivalences

Making Sense of Lens Optics for Crop Sensor Cameras - crop sensor optics

Crop Sensor Optics

Most new photographers often start out with crop sensor cameras because they are usually less expensive. But as you become more advanced does it make sense to upgrade to a full frame system? If you are thinking about upgrading is there a reasonable upgrade path?

For example, should you buy full frame lenses to use with your crop sensor body? It seems so confusing and to be fair, it is a little complicated and the simple rules of thumb don’t tell the whole story. Rather than look at the differences in camera sensors themselves (they are all pretty good), let’s try to make sense of the lenses themselves.

Making Sense of Lens Optics for Crop Sensor Cameras - different lenses

Similar focal length lenses – the Olympus micro 4/3rds 40-150mm f/2.8 (80-300mm equivalent) and Canon’s 100-400mm f/4.5-5.6 (for full frame).

Lens sizes

If you are looking at lenses you will see many different focal lengths and apertures. Even from the same manufacturer for the same camera body, there are often different aperture and focal length combinations. Since an important part of photography is optics, how can you begin to compare lenses for different size sensors? How do the lenses relate to the camera body you are looking at?

Making Sense of Lens Optics for Crop Sensor Cameras - two lenses for comparison

Nifty 50mm (full frame on the left) and micro 4/3rds 25mm (50mm equivalent) on right.

Going further, how do different size crop sensors affect lens optics? Is an f/2.8 lens on a crop sensor camera actually f/2.8 lens or is it something else? What about bigger format cameras? Why do the smaller apertures (f-stops) seem so big but the images so gorgeous with great background separation and bokeh?

This all relates to lens optics and crop sensor equivalences, one of the great mysteries of photography that most photographers don’t really understand.

Lens Optics Basics

To understand lens optics you need to understand what a lens does to the light coming into it. The light coming through a lens actually inverts, flipping the image upside down. The light then projects onto the digital sensor after passing through the lens. 

Making Sense of Lens Optics for Crop Sensor Cameras - diagram of lens focal length

Focal length and image flip onto the sensor.

Most lenses are defined by the focal length and maximum aperture. The higher the focal length, the closer distant objects seem. So, for example, sports and bird watchers typically want much larger focal lengths to get in close.

Lower numbers widen the field of view to make more things fit within the image (wide angle lenses) and are often the tools of the trade for landscape photographers. In 35mm equivalents, a 200mm lens is a long lens and a 20mm lens is a very wide lens.

Making Sense of Lens Optics for Crop Sensor Cameras - aperture diagram

Relative aperture size illustration.

The aperture f-stop number represents the size of the iris or hole in the lens. A lens will be rated based upon the largest aperture the iris can open. The more light you let in, the faster the shutter speed you will need. Because of this property, larger maximum aperture lenses are called faster lenses. For example, an f/2.8 lens is considered pretty fast and an f/5.6 lens (think kit lens) would be considered pretty slow.

Optical Math

Let’s keep the geeky math minimal, but it really helps understand lens optics. 

Focal length is not a measurement of the actual length of a lens, but a calculation of an optical distance from the point where light converges to form a sharp image on the digital sensor at the focal plane in the camera. Aperture, on the other hand, is the size of the hole created by the iris in the lens. Aperture is geometrically related to the focal length of the lens. For example, an f/2.8 lens on a 100 mm focal length lens is 100 divided by 2.8 = 35.7 mm. As the lens focal length dictates the size of the aperture, it is independent of the size of the sensor but dependent on the focal length.

Making Sense of Lens Optics for Crop Sensor Cameras - similar lenses

Utility lenses covering a similar range – the Canon 24-105mm f/4, and the Olympus 12-40mm Making Sense of Lens Optics for Crop Sensor Cameras f/2.8 (24-80mm equivalent).

Zoom lenses may have more than one aperture because the iris doesn’t get bigger as the lens gets longer. Since it is a math relationship, the longer focal length with the same iris opening makes the aperture smaller. More expensive zoom lenses have the same aperture for the entire range but that is a bit of an engineering feat as the iris must get larger as the lens zooms to a longer focal length.

Camera Sensor Format Refresher

In the golden age of film photography, there were multiple formats dictated by film stock. One of the more common sizes was 35mm film dictated by sprocket film stock that was 34.98 ±0.03mm (1.377 ±0.001 inches) wide. Back in the film days, there were multiple formats too, with larger and smaller film stock available that also affected lens sizes and performance.

When digital sensors were originally developed for still cameras, larger sensors were prohibitively expensive, so smaller sensors were used. There is a wide range of sensor sizes and this variety of sensor sizes affects the mechanics of how lenses on cameras operate.

When a sensor is close to the size of 35mm film stock, it is called full frame. Anything smaller is called a crop sensor. Anything bigger is generally called medium format although there is a lot of variability in sizes larger than full frame. Sensors not only vary in size but also geometry.

Making Sense of Lens Optics for Crop Sensor Cameras - crop sensor sizes

Crop sensor relative sizes

Sensor sizes

Generally speaking, a full frame sensor is in the shape of a rectangle that is roughly 36mm x 24mm which is a length to width ratio of 3:2 covering an area of 862mm sq. Conversely, a micro 4/3rds crop sensor is 17.3mm x 13mm (ratio of 4:3) covering an area of 224.9mm sq. A Nikon/Pentax APS-C crop sensor is 23.6mm x 15.7mm (ratio of 3:2) covering an area of 370mm sq, whereas a Canon APS-C sensor is 22.2mm x 14.8mm (ratio of 3:2) but only 328.5mm sq. Larger formats (bigger than full frame) tend to be square.

Many times the crop factors are calculated by the size of the diagonal distance from corner to corner of the sensor.  For example, a full frame sensor is twice the diagonal as a micro 4/3rds sensor, therefore the crop ratio is 2x. For a Nikon APS-C crop sensor the ratio is 1.5x and for a Canon APS-C crop sensor, it is 1.6x.

Making Sense of Lens Optics for Crop Sensor Cameras - sensor footprints and sizes

Comparison of the sensor footprints

Square versus Round

Lenses are round whereas sensors are rectangular or square. So, all cameras cut off part of the image because the round lenses project a circular image on the sensor which is a rectangle. This means that the edges of the image circle are cut off.

Camera manufacturers design their lens/camera combinations so that the entire sensor gets great coverage from the image circle (this is called covering power). This can create problems when you have a mismatch between the sensor size and the size of the sensor for which the lens was made.

Making Sense of Lens Optics for Crop Sensor Cameras -

Image circle with full frame and micro 4/3 frame overlaid

So, How Does Crop Factor Affect Images?

There are lots of factors that affect your images. The sensor size does affect images, but so does focal length and aperture size but those are physical properties of the lens and are not affected by the crop factor. At least not directly.

To illustrate the effect of crop sensors on light gathering and focal length, a series of test images were set up (these are not overly scientific but more illustrative). Using an Olympus EM1 Mark II (Micro 4/3rds sensor – 2 times crop factor) and a Canon 5D Mark IV (full frame).

Making Sense of Lens Optics for Crop Sensor Cameras - Olympus camera

Olympus EM1 Mark II, micro 4/3rds camera

Making Sense of Lens Optics for Crop Sensor Cameras - Canon camera

Canon 5D Mark IV full frame camera.

To illustrate the focal difference conversion and the light gathering conversion, the cameras were set up side by side using only the focal length conversion. The geometry of the sensors is not exactly the same so they have been cropped to match each other (8×10 ratio).

Making Sense of Lens Optics for Crop Sensor Cameras - two cameras shooting the same scene

Camera size comparison (full frame on the left, micro 4/3 on the right)

Both cameras were targeted at the same vista.

Making Sense of Lens Optics for Crop Sensor Cameras - side by side cameras

Test setup side by side cameras.

Rules of Thumb Versus Reality

Focal lengths are commonly converted into equivalents for full frame sensors to give the same the field of view by multiplying the focal length by the sensor’s diagonal ratio. For example, a 25mm lens on a micro 4/3rd sensor is the equivalent of a 50mm lens on a full frame camera (crop factor is 2:1).

A Canon EFS (crop sensor) lens to match a 50mm lens is 31mm. This works in reverse too. If you put a full frame lens on a crop sensor camera body, the focal length is multiplied (the same 50mm lens becomes like a 75mm lens on a crop sensor). This rule of thumb works.

Editor’s note: The optics are not the same, but this is a generally accepted method of understanding crop sensors.

Making Sense of Lens Optics for Crop Sensor Cameras - two photos of a bridge

At 24mm equivalents – same shutter speed and ISO, full frame on left and Micro 4/3 on the right (both at f/4, ISO200, 1/160th).

Aperture and Depth of Field

Another rule of thumb that doesn’t work so great is to add a stop or two for the aperture (depending upon the crop). Why doesn’t it work? Well, there is more at play here.

The aperture affects the light gathering ability of a lens but with a crop sensor camera, the smaller sensor causes the depth of field (area in focus) to be larger.  What that means is that an f/2.8 lens at 200 ISO sensitivity should have very close to the same shutter speed on any camera body (there are variations in light meters from one camera body to another). So an f/2.8 lens is always an f/2.8 for light gathering.

Making Sense of Lens Optics for Crop Sensor Cameras - two bridge photos side by side

At 70mm equivalents – same shutter speed and ISO, full frame on the left and Micro 4/3 on the right (both at f/4, ISO200, 1/80th).

To make things more complex is the look of an image. The bokeh on a crop sensor will never be quite as good as a full-frame sensor because the extra area of a full frame sensor changes the depth of field (the amount of the image in focus) relative to a crop sensor. This is not a function of the lens as much as the sensor size. This can be pretty subtle but it is a factor, particularly for portraits.

Making Sense of Lens Optics for Crop Sensor Cameras

At 200mm equivalents – same shutter speed and ISO, full frame on the left and Micro 4/3 on right (f/4, ISO 200, 1/30th).

Making Sense of Lens Optics for Crop Sensor Cameras

At 200mm equivalents – same shutter speed and ISO, full frame on the left and Micro 4/3 on right (f/4, ISO 200, 1/40th).

Full Frame Lenses on Crop Sensor Cameras

Lenses tend to last much longer than cameras with good lenses lasting as long as two or three camera body iterations. So many people go by the adage of investing in glass. So if you are using a crop sensor body that will accept full frame lenses, why not buy full frame lenses until you are ready to buy the full frame body? The answer is not necessarily because it may not be as sharp as your crop lenses even if the lens seems nominally the same size.

Full frame lenses are more expensive than crop lenses but you are often paying for other features including weather sealing and better more durable construction. Because of large differences in sensor sizes, getting full frame lenses on a crop sensor means you are only using the very center portion of the lens but the detail is more concentrated on that area. This can challenge the optical quality of the full frame lenses.

They are often better quality but not enough better to account for the size differences between the sensors. So unless you know you are upgrading your camera imminently, you may not want to use the full frame lenses on crop bodies.

Another consideration is that you have to use the crop factor in reverse.  On a Canon crop body (1.6 crop factor) a 24mm lens becomes a 38.4mm lens. This means that you can’t get as wide of an angle of view on a crop body with wide lenses.

Making Sense of Lens Optics for Crop Sensor Cameras

A full frame lens on a crop body will increase the focal length by the crop factor

Conclusion

There are lots of misconceptions regarding lenses when comparing them across sensor sizes. Understanding the basic function, light gathering capabilities, and geometric relationships can help you compare lenses within camera systems and across sensor sizes.

There are great lenses available for all camera systems that can produce fantastic results. Lenses are as important as the camera body. So when choosing a system, make sure you have the lens selection you need for your particular style of photography.

Read more from our Cameras & Equipment category

Mark C Hughes is a photographer, writer, educator, and engineer that specializes in both portraits of people and pets but also creates stunning landscape and nature photography. He’s an accredited professional photographer (PPOC) and has won awards, including one from National Geographic. Mark has exhibited works and has testified as an expert witness in a trial as a photographer. He has taught photography for a variety of groups and skill sets.

  • A. Dumas

    Nice info, are these lenses yours, they are very dirty, wouldn’t touch those.

  • Mark Hughes

    Haha! Yes, these are my lenses. Not so much dirty as well used and worn. The optics are clean!

  • Toastiejoe

    To boil this down for simple folk like me, is this correct:
    (I’m talking M4/3 vs full frame)
    • 100mm m4/3 is equivalent to 200mm ff, because it crops down to the same picture size? Put another way, I’d have to crop a ff 100mm picture 50% to see the same picture as the 100mm m4/3?
    • If I take a photo then zoom in, with sufficient zoom it loses quality. Is the m4/3 picture already effectively zoomed in, so that it can’t be zoomed as far as the ff picture could be?
    Sorry if that’s not well phrased. Hopefully you get the drift of what I’m asking, which is, is the m4/3 picture therefore lower quality in some sense?

  • Mark Hughes

    Hi Toastiejoe

    You have two comments, and your first comment is correct but your second is not because with the m4/3 although closer is not really zoomed (it is a native resolution and designed to be at that resolution).

    To put in perspective a 20 megapixel m4/3 image would the the same as a zoomed in 80 megapixel full frame image, so your ability to zoom further is governed by the resolution, not the sensor size. Does that help?

  • Spoonie

    Hi, could you clarify what you mean by “the extra area of a full frame sensor changes the depth of field (the amount of the image in focus) relative to a crop sensor.” I don’t believe that’s correct. If I take an image with a 50mm lens, the depth of field will be the same regardless of the sensor size. The formulae for calculating depth of files doesn’t include sensor size, and in a practice example if I take an image with a 50mm lens and then crop the image the depth of field won’t magically change. So perhaps you mean something else here?

  • Mark Hughes

    Hi Spoonie

    Thanks for the comment.

    I could have worded it slightly better but the concept still holds. The depth of field relates to the aperture only. Aperture is a mathematical relationship to focal distance. When using equivalents between crop and full frame sensors you are correcting for field of view but that doesn’t change the physical aperture. To correct for that you end up realizing you are using a smaller aperture. Remember a 50mm lens on a full frame sensor corresponds to a 25 mm lens on a m4/3 sensor. Does that help clarify?

  • Toastiejoe

    Yes, that clears it up nicely

  • wireways

    Mark, you say “The more light you let in, the slower the shutter speed you will need” – the opposite is true, no?

  • Mark Hughes

    Hmmm…., I found the reference. You are correct, it should say “The more light you let in, the faster the shutter speed you will need.”

  • thanks for picking that up, I should have caught that one – fixed!

  • LOL if your lenses aren’t getting dirty you aren’t shooting enough!

  • miker33

    Yes, DoF does indeed change relative to the crop factor. If you put a 70-200mm f2.8 on a full frame and a crop sensor, both at f2.8, and zoom the full frame so they both capture the same image, the crop-frame will have greater DoF. In practice, you actually have to use the crop factor on *both* the aperture and the focal length to get the same photo. So in the example above, 112mm @ f4.5 on a full-frame camera looks the same (same field of vision, same DoF) as 70mm @ f2.8 on a crop camera. Not trying to hijack Mark’s article, but Tony Northrup has a great video on Youtube on this, actually showing the differences.

  • David Gee

    Thanks Mark for a great article and thanks to everybody for their comments, clarifications and questions. I am now struggling a little less with concepts of DOF and the variation according to sensor size. I am aware that I get less depth of field on my d750 than on my d500 and I have often struggled with why this is so. The article and comments help. Still can’t come at the idea that f4.5 on a full frame sensor camera is equivalent to f2.8 on a crop sensor camera. I guess I see this from a DOF perspective as a theoretical construct, but an f4 lens for example performs the same way regardless of sensor size except as regards DOF which I think is one of Mark’s main points ( I hope I have got that!)

  • Mark Hughes

    Excellent! I appreciate the feedback

  • Mark Hughes

    I am familiar with The Northrup’s website bit you have to be really careful over applying the crop factor to all aspects of photography. It is correct about certain aspects but doesn’t really talk about light gathering capability of the lens. The focus more on the impact on the image but not on the optics of the lens. Thanks for the comment

  • Alan Moore

    You need to explain this properly! DoF is a function of focal lenght, F/stop and subject to lens distance. The DoF changes because to get a similar image in a crop sensor camera with the same lens it would require you to increase the subject to lens distance which then increases the DoF because the further away your subject is the more depth DoF there is. The DoF of 50mm lens @ f/4 focused at 3 feet is the same no matter what camera it is mounted on. Because with that same lens when mounted on a crop sensor camera it becomes a good portrait lens simply because you have to move away from the subject to get a good portrait that fills the frame if you were to do this on a full frame camera you would run the risk of the subject’s nose looking distorted. I hope this helps to clarify some of the confusion

  • Mark Hughes

    Thanks for the comment Alan, I intentionally didn’t focus on the Depth of Field aspect because it sometimes confuses people. You are correct that in order to get the same background separation, bokeh or depth of field from a crop sensor as compared to a full frame sensor you need to correct the aperture. However, that is a modification does not apply to the light gathering ability only to image appearance. My article was more focusing on the optics rather than the image appearance.

  • Jack

    There is NO difference in depth of field between FX and DX. if you adjust your the camera positions so that both sensors show the same image filling up each sensor then DOF is the same. The apparent DOF difference is Ed on different image sizes on other two sensors.

  • Jack

    No that is incorrect!

  • Jack

    The phrase,”apparent DOF difference is Ed on different”, should’ve said “apparent DOF difference is based on different”.

  • Mark Hughes

    Hi Jack…. ummm, what part did you think was incorrect? I don’t know what your objecting to.

  • Jack

    DOF same with FX or DX with same focal length.

  • Jack

    See my othe more detailed comment.

  • Jack

    Alan, Better explanation than mine, but same premise that FX/DX same DOF if you fill each frame with same image you have to move point of view.

  • Maurice Hayward

    David Gee……….In response to your above article, the reason for the difference in aperture size between the two is that as the M4/3 lense has a F2.8 and the F/F has the equivalent f4.5 is that many people / articles omit to say that the aperture is also 2x that of a full frame to give the same result.
    Hope that helps you understand.

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