Note:
Focal Length Extend ability:
Focal Length Reduce ability:
Getting too Technical - the Thin Lens and Thick Lens Model Formula
FoV = Field of View in degrees Sw = Width of sensor in m (0.036 for FF) Fl = Focal Length in m (so 0.2 for 200mm lens) FoV of 100mm lens on FF sensor: 2 * atan (0.036 / (2 * 0.100)) = 20.4079 degrees from FoV to Fl: 0.036 / (2 * tan(20.4079 / 2)) = 0.1 m Width of field D = Distance to measure width at (measured from sensor plane) L = Measured width of field at distance D (in same units as D, m) L = 2 * D * tan(FoV / 2) ---- at 10m: L = 2 * 10 * tan(20.4079 / 2) = 3.6m (fill the frame horizontally at 10m) MFD = Minimum Focus Distance, measured from sensor (in same units as L,D,Sw so say m) MaxMag = Maximum magnification, how big an object is on sensor wrt real life (as a ratio) Lmfd = Field Width at MFD Lmfd = 2 * MFD * tan((2 * atan (Sw / (2 * Fl)))/ 2) Lmfd = Sw / MaxMag ====== Sw / MaxMag = 2 * MFD * tan((2 * atan (Sw / (2 * Fl))) / 2) ====== Fl = 1 / (2 * (tan((2 * atan(Sw / (MaxMag * 2 * MFD))) / 2) / Sw)) ======================= Example 1: Nikon 70-200 f2.8 II: MFD = 1.4, MM = 0.12 Fl = 1 / (2 * (tan((2 * atan(0.036 / (1.4 * 2 * 0.12))) / 2) / 0.036)) = 0.168m
Effective focal length (at minimum focus distance) = Minimum focus distance [mm] / (Maximum reproduction ratio + (1/(Maximum reproduction ratio)) + 2) ------------- DA 16-85mm MFD = 350mm Max reproduction ratio = .26 Focal length = 350 / (.26 + (1/(.26)) + 2) = 57mm DA 18-135mm MFD = 400mm Max reproduction ratio = .24 Focal length = 400 / (.24 + (1/(.24)) + 2) = 62mm A 135mm f2.8 MFD = 1200mm Max reproduction ratio = .15 Focal length = 1200 / (.15 + (1/(.15)) + 2) = 136mm DA 18-270mm MFD = 490mm Max reproduction ratio = .26 Focal length = 490 / (.26 + (1/(.26)) + 2) = 80mm DA* 50-135mm F2.8 124 mm DA*60-250mm MFD = 1100mm Max reproduction ratio = .15 Focal length = 1100 / (.15 + (1/(.15)) + 2) = 125mm DFA*70-200mm MFD = 1200 Max reproduction ratio = .13 Focal length = 1200 / (.13 + (1/(.13)) + 2) = 122mm Tamron 70-200mm F2.8 Macro MFD = 950 Max reproduction ratio = .32 Focal length = 950 / (.32 + (1/(.32)) + 2) = 174mm Canon EF 70-200 f2.8 III MFD = 1200 Max reproduction ratio = .21 Focal length = 1200 / (.21 + (1/(.21)) + 2) = 172mm Nikon 70-200 VR MFD = 1100 Max reproduction ratio = .21 Focal length = 1100 / (.21 + (1/(.21)) + 2) = 157mm Nikon 70-200 VR II MFD = 1400 Max reproduction ratio = .12 Focal length = 1400 / (.12 + (1/(.12)) + 2) = 134mm Nikon 70-200 E MFD = 1100 Max reproduction ratio = .21 Focal length = 1100 / (.21 + (1/(.21)) + 2) = 157mm Nikon S 70-200 Z MFD = 1000 Max reproduction ratio = .2 Focal length = 1000 / (.2 + (1/(.2)) + 2) = 138mm Sony GM 70-200 MFD = 960 Max reproduction ratio = .25 Focal length = 960 / (.25 + (1/(.25)) + 2) = 153mm RF 70-200 MFD = 700 Max reproduction ratio = .23 Focal length = 700 / (.23 + (1/(.23)) + 2) = 106mm Tamron G2 70-200 MFD = 960 Max reproduction ratio = .16 Focal length = 960 / (.16 + (1/(.16)) + 2) = 114mm DA 55-300mm WR MFD = 1400mm Max reproduction ratio = .28 Focal length = 1400 mm / (.28 + (1/(.28)) + 2) = 239mm DA 55-300mm PLM MFD = 950mm Max reproduction ratio = .3 Focal length = 950 mm / (.3 + (1/(.3)) + 2) = 169mm DA*300 MFD = 1.4 m = 1400mm Max reproduction ratio = 1:4 = .25 Focal length = 1400 mm / (.25 + (1/(.25)) + 2) = 224mm DFA 150-450mm MFD = 2000mm Max reproduction ratio = .22 Focal length = 2000 / (.22 + (1/(.22)) + 2) = 296mm Sigma 150-500mm MFD = 2.20 m = 2200mm Max reproduction ratio = .19 Focal length = 2200 / (.19 + (1/(.19)) + 2) = 295mm
for (distance, angle of view, equivalent 135 format focal length) Angle of view calc for different format (like 75mm on 6×6 camera is like 50mm on full frame camera)
Hand Measure | forearm blend front | 20 | 24 | 28 | 30 | cow stretch | cow pose=25 deg | 1 fist=10 deg | 3 finger for 5 deg fr 300mm | (1 finger for 1 deg fr 800mm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Focal Length (mm) | 8 | 14 | 18 | 20 | 24 | 28 | 30 | 35 | 50 | 85 | 90 | 135 | 200 | 300 | 400 | 600 | 800 | 1200 | 1600 | 2400 |
Horizontal (°) | 132.08 | 104.26 | 90.01 | 83.98 | 73.75 | 65.48 | 61.93 | 54.44 | 39.6 | 23.92 | 22.63 | 15.19 | 10.29 | 6.87 | 5.16 | 3.44 | 2.58 | 1.72 | 1.29 | 0.86 |
1.5x APSC (mm) | 12 | 21 | 27 | 30 | 36 | 42 | 45 | 52.5 | 75 | 127.5 | 135 | 202.5 | 300 | 450 | 600 | 900 | 1200 | 1800 | 2400 | 3600 |
1.5x horizon | 112.63 | 81.21 | 67.39 | 61.93 | 53.14 | 46.4 | 43.61 | 37.86 | 27 | 16.08 | 15.19 | 10.16 | 6.87 | 4.59 | 3.44 | 2.3 | 1.72 | 1.15 | 0.86 | 0.58 |
Vertical (°) | 112.63 | 81.21 | 67.39 | 61.93 | 53.14 | 46.4 | 43.61 | 37.86 | 27 | 16.08 | 15.19 | 10.16 | 6.87 | 4.59 | 3.44 | 2.3 | 1.72 | 1.15 | 0.86 | 0.58 |
Diagonal (°) | 139.42 | 114.19 | 100.49 | 94.51 | 84.07 | 75.39 | 71.6 | 63.45 | 46.8 | 28.57 | 27.04 | 18.22 | 12.35 | 8.25 | 6.2 | 4.14 | 3.1 | 2.07 | 1.55 | 1.04 |
The system of angular measurement used by astronomers is based on divisions of the circle. The circle is divided into 360 degrees. Degrees are divided into 60 minutes of arc, or arc minutes, and each minute is divided into 60 arc seconds. The accompanying illustration shows how you can use your hand to make rough estimates of angular sizes. At arm’s length, your little finger is about 1 degree across, your fist is about 10 degrees across, etc. (http://astrofix.net/2010/03/19/85/)
telescope formulas: (ref: http://www.astro-tom.com/technical_data/useful_formulas.htm)
// ref: http://www.tawbaware.com/maxlyons/calc.htm // excel : fovh=ROUNDUP((2*ATAN($filmWidth/(2*FocalLength))*180/3.1415),2) // PI ~ 3.1415 function dec1(aNumber) {return (rnd(aNumber,1));} function compute_fov() { var film_width = 36; var film_height = 24; var film_diag; var f = document.fov_calculator; var flen = f.flen.value; var flen_mult = f.flen_mult.value; if (isNaN(flen_mult) || flen_mult<=0) { f.flen_mult = 1; flen_mult = 1; } //Account for focal length multiplier (actually, a film/sensor size multiplier) film_width = film_width/flen_mult; film_height = film_height/flen_mult; film_diag = (Math.sqrt((film_width * film_width) + (film_height * film_height))); var fov_h = (2 * Math.atan(film_width / (2 * flen)) * 180 / Math.PI); var fov_v = (2 * Math.atan(film_height / (2 * flen)) * 180 / Math.PI); var fov_d = (2 * Math.atan(film_diag / (2 * flen)) * 180 / Math.PI); f.fov_h.value = dec1(fov_h); f.fov_v.value = dec1(fov_v); f.fov_d.value = dec1(fov_d); }