This has been stimulated by discussion in the threads about 600mm f/6.3 vs 500mm f/5.6 telephoto lenses. It is usually thought that the larger f-number of the longer lens means either a slower shutter speed or introducing more noise by having to increase the iso, which is a disadvantage for the longer lens. I’ll show that the 600mm doesn’t suffer from those apparent disadvantages.

I am analysing the situation that is the usual one of using telephoto lenses with the output Images of crops blown up to the same viewing or printing size from different focal lengths and apertures, or from smaller sensors or crops blown up to the same size images from larger sensors.

**Crop vs Full-Frame Sensors**

Let’s start in our comfort zone with something that most of us do know from practice and maybe as well from theory: the images from smaller sensors are inherently noisier than large ones and have lower dynamic range

*when viewed at the same image size*. The qualitative reason for this is that the image from the smaller sensor has to be enlarged more to give the same size image as from a larger sensor. This amplifies the noise in the image as well as any defects and lowers effective dynamic range.

In terms of physics, there is noise in an image because of fluctuations in the amount of light or number of photons,

*n*, hitting the sensor. From statistics (the Poisson Distribution), the signal to noise (S/N) = sqrt(

*n*). The more the light, the higher sqrt(

*n*) and so the better S/N. We can calculate the difference in number of stops (ev) using logarithm to base 2, log(2), applied to the change in area of sensors. For a crop factor of 1.6 for FF vs APS-C.

Number of stops = log(2)(1.6x1.6) = 1.36ev.

So, all else being equal, a crop APS-C sensor has 1.36 stops more photon noise than full frame. That is equivalent to setting the iso of the crop 2.56x higher in terms of noise (1.6x1.6, and increasing the iso increases noise). Or, we need a lens that is has an f-number 1.36 wider to let in more light to compensate.

A common mistake is to consider just the f-number of the lens as being the only factor that determines the amount of light in an image. The f-number does determine the intensity of light hitting a sensor, but the degree of enlargement of the image from the sensor is another key factor.

**Cropping**

Cropping, as we know from practice, increases noise in an enlarged image, and it follows the same principles as crop vs FF sensors. We need to work at progressively lower isos to keep noise under control the more we crop.

**Using a 1.4x and other Teleconverters**

Putting a 1.4xTC on our telephoto increases its focal length by 40% but increases its f-number by one stop. People sometimes complain that using a larger f-number at the same shutter speed means increasing the iso to compensate and so increases the noise. Alternatively, it is thought we can maintain the iso by lowering the shutter speed, but that could be bad. But, increasing the focal length by 40% increases the area of the image by 1.4x1.4 = 2 times. So, we have to blow up the image from lens without the TC 2x in area to be the same size as with the TC. This is equivalent to lowering the iso noise with the TC by = log(2)(2) = 1 stop.

*So, double the iso at the same shutter speed when shooting with a 1.4xTC and we will have only the same noise as without the TC and twice the number of pixels on target blown up to viewing size*!

Fewer people know that.

**500mm f/5.6 vs 600mm f/6.3**

Let’s compare the size of images produced. The image of an object from the 600mm is 1.2x1.2 times larger in area. So, the 500mm image has to be enlarged 1.44x in area, which is log(2)(1.44) = 0.53 stops. The image of the 600mm f/6.3 lens is 0.33 stops dimmer than the 500mm f/5.6. However, raising the iso by 0.33 stops when working with it at f/6.3 and the same shutter speed as the 500/5.6 actually gives an improvement in noise 0.53-0.33 stops = 0.2 stops better.

*So, all things being equal, shooting the 600mm f/6.3 at the same shutter speed as a 500mm f/5.6 but at 0.33 stops higher iso puts 44% more pixels on target and slightly better noise when viewing images at the same size!*

**Diffraction effects**

### Diffraction, Airy Disks and implications

Two points of light are clearly resolved when they are separated by distances that are much larger than the radius of the disk. As the separation decreases, the disks start overlapping and the resolution decreases. When the separation is the same as the radius, the disks have coalesced. Closer...

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Very briefly, the diameter of the 600mm lens is actually slightly larger than that of the 500mm.

Diameter of 600mm f/6.3 entrance pupil = 95.2mm.

Diameter of 500mm f/5.6 entrance pupil = 89.3mm.

This means that when even when fully diffraction limited, the the 600mm gives better resolution. Its Airy disk is 6.3/5.6 = 1.125x larger but the linear separation is 1.2x larger.

*In conclusion*, I would prefer a 600mm f/6.3 zoom to a 500mm f/5.6. Although, for primes I would prefer the larger field of view of the 500mm, whereas the 600mm zoom can be zoomed out to 500mm or shorter if needed.