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Understanding how lenses work: Focal Length, F-Stop, Aperture & Crop Factor

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If you do not have at least a basic understanding of how lenses work then you are unlikely to ever get the most out of your digital single reflex (DSLR) camera, Mirrorless Interchangeable Lens (MILC) camera or even compact digital camera. You will definitely not get the most out of using your camera in manual modes as well. This blog provides a level of technical understanding of concepts like focal length, field of view, sensor size, crop factor, aperture, F-stop, and other critical concepts for you to get the best out of the cameras manual modes and enable you to buy the correct lenses for your particular needs.

Once you have read this article you might want to read Using your camera’s manual mode: Aperture, F-stop, ISO and shutter speed.


Focal Length


A lens’ focal length is the distance between the lens’ optical center and that lens’ camera’s image sensor (or film plane), when the lens is focused at infinity. If we consider the focal-length-basic-explanation diagram, you can see that the Object Distance is simply the distance of the object being photographed (and focused on) from the lens. The optical center of a lens can generally be seen as the point within a lens where the light rays from two different sources of the image entering the lens cross over. In contrast to the object distance, the focal length of the lens is the same as the Image Distance, which is the distance between the lens’ optical center and the image sensor.


Field of view


The field of view of a lens is the amount of the image that can be seen through the lens. Lenses that have shorter focal lengths (i.e. everything looks smaller / less magnified / further away) also provide a wider field of view. Similarly, longer focal lengths (i.e. everything looks larger / more magnified / closer) offer a narrower field of view.




This is clearly illustrated in the focal_length_ &_field_of_view diagram above, where you can see that at a 900mm focal length the lens is able to magnify a very distant object, but at the cost of only being able to include a very small amount of the image on the image sensor. Focal length is generally recorded in millimeters, and clearly the larger the number the stronger the magnification of the lens, and the narrower the field of view.


Very importantly for us photographers, field / angle of view also affects the amount of light that can reach the sensor. As explained clearly in the diagram in Using your camera’s manual mode: Aperture, F-stop, ISO and shutter speed, the wider the angle of view the more light that can reach the sensor and the narrower the angle of view the less light that can reach the sensor.



Confucius says…

“Life is really simple, but we insist on making it complicated.

Now that you understand focal length and field of view you could be forgiven for assuming that all you have to do is read the number on the lens in order to know what the focal length of your lens will be, and therefore both how much magnification you will get and how broad / narrow your depth of field will be. Sadly though, refer to Confucius… We will need to detour slightly here to something that actually has to do with the camera itself and not the lens: sensor size.


Sensor size

The size of a cameras sensor is probably the single most important determinate of quality. Manufacturers and retail stores often try to blind one with the megapixels that a camera produces, but actually we need to start with sensor size. In fact, you might want to read this article explaining how increasing megapixels can decrease image quality. Full frame cameras have sensors that approximate that of a film camera 35mm sensor (they measure 36mm x 24mm). Cropped sensor cameras have smaller sensors and tend to be somewhat cheaper (although there can be good reasons other than budget for choosing a cropped sensor camera over a full sensor one).


Digital single lens reflex camera manufacturers tend to all utilize the 35mm approximation for their full frame cameras. However, their cropped sensor cameras tend to vary in size. These cropped sensor cameras tend to adhere roughly to the Advanced Photo System type-C (APS-C) image sensor format, which is approximately equivalent in size to the Advanced Photo System "classic" negatives of 25.1 × 16.7 mm. They therefore have an aspect ratio 3 to 2 (or 2/3 of the full frame sensor size).


The first sensor size diagram gives you an understanding of the actual sensor sizes of a range of cameras. If it is slightly different on your screen then just adjust the photo size so that the orange and indeed all the grey rectangles are 36mm X 24mm and then all the other sensor sizes will be correct. 

The sensor size comparison diagram is not to scale, but gives you insights into the relative sensor sizes of various camera manufacturers. Worth noting is that for all the iphone’s fancy add-ons even the iphone 7 has hardly changed actual sensor size and this means it still performs poorest in low light conditions when compared to Google Pixel and the Samsung S7. And if anyone wonders where Canon fits in on this diagram they are pretty much the same as the Nikon DSLR’s. Full frame Canon cameras have the same sensor size as full frame Nikon cameras, APS-C Canon DSLRs have sensors just a smidge smaller than APS-C Nikon cameras, and Canon also have a few DSLR cameras with a sensor size denoted as APS-H, which is pretty much midway between APS-C sensors and full frame sensors. Dwarfing even the full frame sensors are medium format sensors, which provide unrivalled clarity and image quality (though they come with other limitations).


The Crop Factor

Full frame cameras (i.e. a ‘full size’ 35mm sensor) are not in fact capable of shooting any wider than a cropped sensor camera! This is a misconception that many photographers seem to have. It is merely that lenses are calibrated as if they are on a full sensor camera. So a 100mm lens would have a focal length of 100mm on a full sensor camera. Because cropped sensor cameras have a smaller sensor size, with the same lens it will have a greater magnification and narrower field of view than when that lens is on a full frame camera. They are called ‘cropped sensor’ cameras as only part of the image that is actually being produced by the lens is captured by the APS-C size sensor (but what you see through the viewfinder is still the same as what is being shot in DSLR’s).


So how much is the crop factor? Well, it is directly proportionate to the size of the lens (vis a vis a full frame sensor). A crop factor can be used to calculate the field of view in terms of a standard 35mm sensor (since this is what the numbers on the side of the lens are calculated in reference to). Crop factor can simply be seen as the amount that the number on the side of the lens needs to be multiplied by in order to achieve the actual magnification and field of view through your specific camera. So for my Canon 7D Mark II, which is a cropped sensor camera with a sensor size ratio of roughly 0.62 (i.e. 62% of a full frame sensor size), the multiplier happens to be 1.6X (times). How is this calculated: Full Frame sensor ratio (1, as this is the reference) divided by the percentage of full frame size that your particular sensor is, will give you the Multiplier:

So 1/0.62 = 1.6

I can take my crop factor and multiply this by whatever it says on my lens in order to get the actual focal length / magnification / field of view. So using the above example my 16mm lens on my full frame Canon 5D Mark IV will give me a 16mm focal length / magnification. On my cropped sensor Canon 7D Mark II it will give me a focal length / magnification of 16 X 1.6 = 26mm. Please note that as the crop factor gets larger the field of view becomes narrower!


If I particularly wanted a focal length of 16mm (due to needing that magnification and/or field of view) then I would either use my full frame camera with the 16mm lens or my cropped sensor camera with a 10mm lens (10 X 1.6 = 16mm).


Any wildlife photographer worth their salt will tend to have both a full frame and cropped sensor camera. The full frame will always have that advantage in quality, provided the animal or bird isn’t too far away. However, the cropped sensor camera comes with a huge advantage in that it has this ‘built in’ 1.6X multiplier (for Canon). In practical terms this means that the trusty Canon 100-400mm Mark II (under $2000 and 1.59kg), Canon EF 400mm f/5.6L USM Lens (under $1200 and 1.25kg) or the more expensive F4 Canon EF 400mm f/4 DO IS II USM Lens ($under $7000 and around 2.1 kg) has a focal length of 640mm at maximum (400mm X 1.6 = 640mm). On (an already much heavier) full frame camera in order to achieve a 600mm focal length equivalent at the same aperture F-stop, a lens such as the Canon EF 600mm f/4L IS II USM Lens would be required. This costs around $11500 and weighs in at a hefty 3.92 kg, which is actually about a third less than the mark I version!


Now if you are a gazillionnaire and are shooting out of a stationary car window or car mounted tripod then the full frame option might be viable. However, if you are bouncing around in a Landy, or needing to drag it along on a walking safari you might think otherwise! And then of course you have to ask the question as to how still you can hand hold that 600mm and for how many shots! Don’t get me wrong, I am a huge fan of the Canon 600mm lens, without doubt their sharpest super telephoto. But I prefer to use it on a bean bag or tripod when sitting calmly at a lake or watering hole.



Understanding the F-Stop


The F-stop is the funny number hanging around on the lens, directly after the focal length (which is always in millimeters). It may have an F followed by a number (e.g. F4.0) or it may be displayed as a ratio (e.g. 1:4). The lens F-stop can be seen as the same thing as the focal ratio, f-ratio or relative aperture, which is actually not an absolute value but rather a ratio between the lenses focal length and diameter of the entrance pupil (effective aperture).


Okay, before you mind feels completely scrambled let’s consider this information in relation to my Canon 200mm F2 lens:


focal length / lens diameter = F-stop


So if we go back to high school and multiply both sides of the equation by the lens diameter and divide both sides by the F-stop we now have:


focal length / F-stop = lens diameter


So, 200mm / 2 = 100mm. This is the diameter of the lens when wide open (maximum aperture). By the way the lens (like most) will stop all the way down to F32, but the value that you will see on the lens is that of the maximum aperture (i.e. when the lens diameter is at its maximum).


Let us consider another example, this time with my Canon 50mm F1.4 lens.


focal length / F-stop = lens diameter


It obviously has a focal length of 50mm and at this (1.4) F-stop it will have an entrance pupil diameter of 35.7 mm.


So although the 200mm F2.0 lens actually has a smaller aperture ration (larger F-stop number) of F2.0 versus the 50mm F-stop of 1.4, in terms of absolute aperture size the 200mm lens is much larger, and this size advantage is increased enormously when we consider the actual aperture and the amount of light that it is letting in.


Back to school again! Area of a circle = πr2

(with r being the radius, which is half of the diameter and π being pi, which approximates 3.14)


Max. aperture area of Canon 50mm F1.4 = 3.14 (35.7/2)2 = 1000.4 square millimeters

Max. aperture area of Canon 200mm F2 = 3.14 (100/2)2 = 7850 square millimeters



Why do the F-stop numbers get bigger as the lens aperture gets smaller?

Funny thing about lens apertures (F-stop values): as the actual lens aperture (the diameter of the lens) gets smaller so the F-stop or aperture ratio gets bigger. For each full F-stop the amount of light being let into the lens is halved.


This can be clearly demonstrated in the diagram Lens aperture at various F-stop values where the same lens is stopped down (contracted) and the F-values increase.




But let us quickly work our own example, again using my 200mm F2 lens, as we have already calculated all its critical measurements! When this lens is wide open at F2, and it has a diameter of 100mm and a focal length of 200mm. Let us assume for a second that the shutter speed is at a constant that I am happy with, but my pictures are (going to be) overexposed. I decide to ‘stop down’ in order to halve the amount of light being allowed through my lens. So I change the camera setting from F2 to F2.8, which happens to amount to half the amount of light (Area of a circle = πr2 )


200mm / 2.8 = 71mm, which is now the diameter of the lens.

So now you should have a deeper level of knowledge of Focal Length, F-Stop, Aperture & Crop Factor! I hope this brief tutorial has been useful, and in order to convert this into a more practical ability to better use your camera and lenses I strongly recommend that you read Using your camera’s manual mode: Aperture, F-stop, ISO and shutter speed, which follows on from this.

We at Cameraverse hope you now have a better understanding of these concepts and that it empowers you when making a decision on which photographic equipment you wish to purchase. As always, feel free to contact us here at Cameraverse if you would like some advice on what action camera will best suite your needs!


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