What Is Reach, Really?

Nikon Z5ii, AF-S Nikkor 300mm f4 D

What is reach? It's a rather misunderstood thing, way too often associated with the use of crop frame cameras, which is often correct, but not for the reasons that most think.

I usually talk about Pixels on Ducks to put a perspective on reach, because at the end of the day, reach is how many pixels you put on a given subject when shooting with a given focal length and subject/camera distance. What really matters in this regard in the camera is the pixel pitch, or how large the pixels are, as smaller pixels mean more pixels covered by the image projected onto the sensor by the lens, and that DOES NOT change regardless of the sensor size, only with the pixel pitch of said sensor. A 300mm lens projects the same sized image on the sensor so long as the subject is the same size and at the same distance (NB - this gets funky at very close ranges with Internal Focusing lenses, but that's because they lose that 'same focal length' property when focusing close, IF lenses and focus breathing are a post for another day, lets stick with wildlife-esque distances for the reach discussion, as those are most relevant). Note the image projection onto the sensor takes into account only subject size, lens focal length and subject/camera distance (actually distance to the nodal point of the lens optics), it does not at all care what size the sensor is.

Pixel pitch is the physical size of the sensor site/pixel (usually square, so only one dimension is given), pixel density is the number of pixels in a unit area, the two terms are functionally interchangeable, although fill factor also impacts pixel density. Fill factor is how much space there is between pixels as a ratio of pixel size and with modern microlens-topped sensors it's just about the same as effective pixel pitch thanks to the microlens  covering the unused space on the sensor and directly otherwise wasted light into the sensor site. For our uses in terms of reach, effective pixel pitch and pixel density are all we care about. 

For example, if you shoot a 300mm lens at an arbitrary duck at 15m from the camera on a 102MP 33x44mm camera (say the Fuji GFX100), a 61MP FF camera (say the A7RV) and a 26MP APS-C camera (say the Fuji X-H2s), and crop each resulting image down to the same pixel dimensions, the resulting image will be the same in terms of framing and resolution as all 3 sensors have the same pixel pitch (they are actually quite closely related sensors, which is why I used this specific set for comparison purposes).  

So why is crop associated with reach? For two reasons, one correct and one incorrect. The first is simply the focal length 'multiplier', which really isn't one, it just looks like one through the viewfinder. It's a crop of the projected image, not a multiplier of the lens focal length (that requires an optical teleconverter). 

The APS-C sensor is smaller and only sees a portion of the frame that the larger Full Frame sensor does. Going from FF as the baseline into a typical 1.5x crop APS-C you are cropping from that 300m of view into the equivalent of a 450mm lens on FF's field of view. But you are also losing overall resolution if the pixel pitch of each sensor is the same. Same size pixels, less sensor area = less overall pixels and less resolution as a result.

So what gives? Well typically crop sensors also have higher pixel density than their equivalent FF bodies. Go from my Z5ii to a D7200 and I'm still getting 24MP images, but now at the field of view that the 1.5x longer lens would have on the larger sensor camera. So in this specific case the D7200 has more reach than the Z5ii. That the crop sensor cameras have more reach than the larger sensor cameras is a general rule of thumb derived solely from them also having higher pixel density sensors, which is often, but not always true. In particular the 60-ish MP FF bodies (and 100MP Medium Format) all have pixel densities matching or exceeding 26MP APS-C sensors (most match, the new A7RVI exceeds due to the slightly higher density 67MP sensor vs the 26MP and 61MP sensors). 

The 25MP m43 sensors pretty much match the 40MP Fuji sensors for highest pixel density available today, with the 20MP m43 and 32.5MP Canon APS-C sensors next, then the 67MP FF sensor, then that set of Sony/Fuji sensors (26/61/102MP) and Canon 24MP (smaller 1.6x crop sensor and same resolution means slightly higher pixel density than 1.5x sensors), then the 24MP APS-C sensors, and then the 45-50MP FF sensors and Nikon's 20.9MP DX sensor, then everything else smaller. 

You'll note this mostly biases towards either crop (especially m43 where everything current is in the top two buckets) or high-MP FF. The ever so common 24-33MP FF bodies have pixel densities not seen in crop cameras in over a decade (10-14MP APS-C equivalents).

So if you want to put pixels on ducks (which usually also means you want a higher fps and good AF), and you don't have money for high-MP/good AF bodies like the Z8, R5 series, A1's or A7R's, then crop really is what you want for reach. Also if you want to minimize size by using shorter focal lengths, then m43 stands out.

And yes, there are also teleconverters. But TC's cost you light, they are not free. And coincidentally the very same physics applies to crop sensors, so a TC's cost in aperture (1 stop for a 1.4x, 2 stops for a 2x) is very close or identical to the total illumination loss from crop sensors (which closely matches the ISO noise performance tradeoff between formats). That's just over 1 stop for a 1.5x crop and 2 stops for a 2x crop (m43). Note simply cropping an FF image down to APS-C results in the same noise tradeoff as shooting APS-C (noise tracks total illumination of the sensor area used, so cropping is throwing away the extra light the larger sensor gets).

As a result, a TC on a lower pixel density sensor is pretty close to equivalent in results to the same lens without TC on a comparable crop sensor of the same resolution. 24MP FF + 1.4x TC is pretty close to functionally equivalent to 21-26MP APS-C. But TC's have other tradeoffs. First off on DSLR's especially the AF system takes a performance hit (and note on DSLR's the AF systems usually have similar projections between FF and crop, they just cover more of the image frame with AF points on crop, so the AF performance usually doesn't differ much between FF and crop, all other things being equal, ie same AF sensor, same lens aperture, same processing power backing it and same algorithms). On Mirrorless things are different because the image sensor IS the AF sensor, so the larger sensors feed more light to the AF system as well. TC's are also limited in lens compatibility so they are not a fix-all for reach issues on low pixel density cameras. Longer lenses or buying a higher pixel density camera are usually the better choice and when dealing with long lenses it's very often cheaper to buy the camera, especially when talking about faster telephoto primes which often cost multiple of even the most expensive FF pro camera, your typical fast 600mm prime will cost 50-100% of what a Z9, A1II or R1 costs if buying new, let alone how much more they cost than a high-end crop body.