In photography, especially the angle of view (AOV) is interesting. The AOV is the angle that a lens provides for a sensor – it can be specified horizontally, diagonally or vertically.
AOV (°) = 2 * arctan ( sensor_height|width|diagonale (mm) / (2 * focal_length (mm)) )
The formula for getting from a certain focal length (FL) on a non-frame sensor to the frame equivalent focal length is:
equivalent_FL (mm) = true_FL (mm) * crop_factor
The harvest factor can be determined by comparing the diagonals:
crop_factor = full_frame_diag (mm) / your_sensor_diag (mm)
- At the same focal length, a larger sensor (but equal aspect ratio) will give a larger AOV
- For the same sensor dimensions, a smaller focal length gives a larger AOV
- AOV differs in vertical, horizontal and diagonal axes (except for a quadratic sensor where vert and h are the same)
Or in practical terms:
- With a 10mm lens on your 5.6 crop factor sensor, you get an AOV equivalent to that of a 56mm lens on a full screen sensor.
- The same 10mm lens on a 1.6 Crop Factor sensor provides an AOV equivalent to that of a 16mm lens on a full screen sensor.
- A 1600mm lens with a full-frame sensor provides the same focal length as a 1000mm APS-C (1.6-inch cropped) lens or a ~ 285mm lens for your shot.
- A 16mm lens on a full-frame sensor has the same focal length as a 10mm lens on an APS-C camera or a ~ 2.85mm lens at your pick-up point.
- For all other factors, smaller sensors prefer smaller AOVs /
Higher range while larger sensors prefer wider AOVs.
- Among the ignored factors are:
- Pixel density (a 20mm² sensor with 20MP has pixels half as big as
a 40mm² sensor with 20MP) which influences the noise (smaller pixels)
are usually worse at collecting light and therefore contain more noise
- Aperture (f / 4 at a 5.6 crop factor is approximately f / 24 at full aperture
- Physical limitations (eg negatively weighted focal lengths
(-1mm) are not possible)
Why do we use focal lengths (in mm) for lenses? Because AOV is not a function of the lens, but the sensor-lens combination. A lens retains its focal length forever, but depending on which sensor it is mounted on, its AOV varies. (Of course, the image circle that a lens can provide limits its capabilities at some point, so attaching a 3mm smartphone to a medium format sensor does not do much good ;-))
Oh and Why compare it to full screen? Since we needed a metric to compare, we could also use IMAX or Super35 or
1 / (⅔ * π) (inches) If we like.
Now for the actual answer to the question:
Their formula was:
(1365 / 5.6) * 1.6 = 390
Which would mean:
effective_FL / crop_factor_PnS = real_FL_PnS
real_FL_PnS * crop_factor_APS-C = ??
What you calculate is therefore the effective focal length of the lens of your Point & Shoot camera on the sensor of your new camera.
Its 1365mm is already full-screen equivalent, so you can already calculate the APS-C-related true focal length with this value.
1365 / 1.6 = 853.125 (mm)
So you need a lens with this focal length to achieve the same tight AOV with a 1.6 Crop Factor sensor.
Note that the AOV difference is between 100 and 200 mm larger than that between 500 and 600 mm!
Note that as mentioned earlier, 400mm lenses are usually very expensive and are primarily limited to primes (and / or using teleconverters that can disable the AF of your camera if your lens is not fast enough ). This is because it is usually a niche market designed for professionals who want / want the highest image quality most 15,000-euro lenses on 5,000-euro bodies offer in the worst circumstances, a better picture quality than any 500-euro camera. Does that mean that you are a better photographer or that you need this setup? No!
I'm not interested in it, but if you want a modular system with this range, I think μ4 / 3 might be the better choice if you have a limited budget – it offers a 2x crop and 100-400 mm lenses not quite as expensive as a 800mm prime from Canon 😉