Making Sense of Lens Optics for Crop Sensor Cameras

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

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.

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?

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. 

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.

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 slower 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.

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.

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.

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.

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).

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).

Both cameras were targeted at the same vista.

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.

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.

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.

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.

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 at the camera body. So when choosing a system, make sure you have the lens selection you need for your particular style of photography.

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