Intro to Focal Length

Note:

  • all focal length mentioned below are in term of 35mm film equivalent focal length;
  • thus if you use a smaller format camera, you times your crop factor to get the 35mm film equivalent focal length; Eg. for m43 camera, you times 2
  • thus if you use a larger format camera, you divide your crop factor to get the 35mm film equivalent focal length; Eg. for 645 medium format, you divide roughly 1.5

Fisheye Lens

  • There are 2 types of fisheye
    • Circular Fisheye lens, normally cover 180 degree in both vertical and horizontal, and image only cover the circle area of image area while with dark area around edge
      • normally around 8mm (35mm film equivalent focal length)
    • Full frame Fisheye lens, normally only cover 180 degree in horizontal, and image cover the full image area
      • normally range from 12mm to 16mm (35mm film equivalent focal length)
  • Characteristic of wide angle lens photo
    • the significant difference between fisheye range focal length photos and other focal length photos are the off-center-axis curvature distortion of straight lines;
    • that means only the straights lines crossing lens center point will keep straight looks
    • all parellel lines will converge at the the sphere edge of full fisheye image area.
    • circle and oval in the fisheye stays as circle and oval.
  • Applications of Fisheye
    • capture fun of the event environment, and people all around
    • capture full area of sky and landscape
    • capture people/subjects and all the environment behind them.

Wide Angle Lens (14-28mm)

  • wide angle lens are range from 14mm to 28mm
  • Characteristic of wide angle lens photo
    • stronger perspective distortion than how our normal human eye see the world; (of course other animals may see wider than human beings); which means the Front subjects looks extremely bigger than the subjects at the Back, and subjects at the Back looks extremely smaller than the Front subjects.
    • all straight lines in real world will stay straight (in case of ideal pefectly designed rectlinear lens with no physical human design caused extra image distortion - lens distortion)
    • also parallel lines in real world that not perpendicular to lens center light path will look more extremely unparallel, and quickly converge into the vanishing point at the horizon. while parallel lines that are perpendicular to lens center light path will stay parallel (in case of ideal pefectly designed rectlinear lens with no physical human design caused extra image distortion - lens distortion)
    • also circle and oval will looks more unevenly stretch near the edge of photo, and the nearer to the edge, the more stretched the circle and oval will get; thus, circle and oval will not even be idea oval shape, more like water drop shape towards the edge.
  • Application of wide angle lens:
    • make small space looks extreme spacious
    • make Front subject more impact against background
    • capture event and environment in a more human visual way comparing to fisheye lens

Normal Lens (35-70mm)

  • of course, so-called normal lens is refering to how human eye normally see subjects around the environment, as the perpective look is more human see things, such as the front subject vs back subject size difference in the captured image area; thus, normal lens is normal to human only, other animal may not look the same way.
  • characteristics of normal lens photo:
    • no perspective impact, and natural representation of the subjects to our human perception.
    • thus, more pleasant to showcase our daily life and everyday subjects.
    • most prime lens design from this range onwards has almost zero lens distortion, and subject will likely keep their shape in the whole image area.
  • Application of normal lens:
    • showcase of normal subjects in the normal way.

Telephoto Lens (85mm to 300mm)

  • Telephoto lens are range from 85mm to 300mm
  • Characteristic of telephoto lens photo:
    • even less perspective presents in the image, and the perception of distance and space start to disappear.
    • more isolation of subjects from environment due to the narrow viewing angle of the telephoto lens (small Angle of View)
    • depth of field also become narrowed, background becomes more out of focus (more Bokeh)
    • also make subjects at distance appear larger/closer than how our eye normally see.
  • Application of telephoto lens:
    • isolation and emphasis on subjects against environment
    • capture distant subject
    • get closer look of subject when our human eye see things

Super Telephoto Lens (300mm to 800mm)

  • Super Telephoto lens are range from 300mm to 800mm
  • Characteristic of super telephoto lens photo:
    • space and distance perception reference are gone, since extremely less amount of environment is in focus or captured within image area (due to extremely smaller angle of view and extremely narrow depth of field)
    • subjects look more surrealistic as it looks more like floating in space and time, freezed and seperation from our world.
    • make subjects at great dsitance appear larger/closer than what we can imagine normally
  • Application of super telephoto lens:
    • capture distant subject
    • great isolation and emphasis of subjects

Special Ability or add-on Feature of the Lens

  • macro and close-up ability: ability to see things very close to the front of the lens (like short-sight human eyes)
    • the close-up/macro ability are measured in term of magnification ratio - the captured subject size on image area divived by the real world subject size
      • only lens with magnication ratio larger than 1:4 are offically called Macro lens
    • Lens at all focal length can have this ability by adding extension tube or front macro/closeup filter
    • Macro Lens can be any focal length, some common ones are like 50mm 1:1 macro, 100mm 1:1 macro, 180mm 1:1 macro; while wide angle macro lens has like 15mm 1:1 macro, 35mm 1:1 macro
    • However, any focal length can be turned into Macro lens by adding rear extension tube, or adding front macro/closeup filter.
  • Application of macro/closeup ability
    • make extreme small subject look normal or huge size to our human eye
    • capture close up subject
      • most normal focal length can't see things clearly within 30cm
      • most telephoto lens are far-sight, and can't see clearly within 1-2 meters
      • most super telephoto lens are extreme far-sight, and can't see clearly within 5 meters mostly
  • Tilt and Shift ability: lens's position and rotation with relation to image capturing area can be changed
  • Application of Tilt and Shift ability
    • shift ability: change perspective vanishing point, thus control line direction captured
    • tilt ability: make gradient difference of focus distance acrosing image area,
      • so different image area can have different distant subjects all clearly in focus at same time;
      • or different image area can have same distant subjects Not all in focus at the same time
  • all focal length can have tilt shift ability
    • those who have this feature built-in are called tilt shift lens (tilt or shift or both)
    • other lens can have this ability by using a title shift adapter and a smaller format camera
      • Eg. use 35mm format DSLR lens on m43 camera with tilt-shift adapter
  • additional reading:
    • using bigger format lens on a small format camera and a bellow mount system, and that adds extra ability to tilt and shift the image area plane as well; which are quite common in large format photography.

Focal Length Extend ability:

  • ability to extend/increase the focal length of the lens;
  • rear focal length extender (teleconvertor):
    • How rear extender work: it magnified the center portion of lens image area and projected to the same capture image area, thus, it behaves like digital zoom inside camera, it enlarge portion of the image at loss of original image quality, as light pass through additional glass.
    • rear focal length extender's ability is measured in term of “Multiplier”: common ones are 1.4x, 1.7x, 2x, 3x. which multiply the focal length and aperture of the lens; like 200mm f4 lens with 2x teleconver behaves like 400mm f8 lens with same minimum focus distance.
    • rear extender type:
      1. built-in:
        • few photography lens has extender built-in, and almost are for telephoto lens, such as Canon EF 200-400mm f/4L IS USM Lens with Built-in 1.4x;
        • rest this kind of built-in extender lens are television lens for covering sports broadcasting.
      2. standalone extender type :
        • mount at rear of the lens, almost all focal length can use this type, functioning same as those built-in extender but are built seperated.
        • High quality teleconvertors are normally built specifically to match certain good quality telephoto lens.
  • front focal length extender (front teleconveror):
    • front focal length extender are mainly for fix lens cameras, or as cheaper alternative for low end lens.
    • How front extender work: it mounts on the filter thread of the lens, and it behave like telephoto lens itself, it captures narrow angle of view and pass it to the lens next, and the lens itself behave like a rear extender. The front extender's quality directly influence the final image.
    • front focal length extender's ability is measured in term of “Multiplier”: common ones are 1.4x, 1.7x, 2x, which only multiply the focal length of the lens; like 200mm f4 lens with 2x front teleconveror behaves like 400mm f4 lens.
  • Application of focal length extender
    • increase reach of the focal length at loss of image quality (both lens and extender quality matters)

Focal Length Reduce ability:

  • ability to reduce the focal length of the lens;
  • rear focal length reducer (speed booster):
    • to do
  • front focal length reducer (wide angle convertor):
    • to do
  • anamorphic front convertor (1.33x Anamorphic Adapter):
    • basically a wide angle convertor in horizontal area only
    • to do

Focal Length related Charts and Calculators

  • Base the graph of field of view calculation
    • Focal length is proportional to the film/sensor width and heights for same field of view.
  • Thus,
    • for 2x factor, focal length is 2x of orignal, then film/sensor width and heights are 1/2 of original.
    • for digital cropping, shrink the width and height by 1/x, the focal length is increased to x times.

Before Reading

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)

Angle of View per Focal Length (135 format)

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
  • So, to Edge-Touch the Moon, you need at least 2400mm equiv. focal length (about 0.5 degree).

Hand View AngleHand View StarMoon Angle

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)

  • Magnification = Objective Focal Length / Eyepiece Focal Length
    • Example: A 2000 mm focal length telescope using a 20 mm eyepiece yields a magnification of 100 times:
    • Example: Magnification = 2000 mm / 20 mm = 100
  • True Field of View = Eyepiece Apparent Field of View / Magnification of view
    • Example: If we are still using the 20 mm eyepiece from the previous example on the same telescope, and we know from looking up in the manufacture's specifications that the eyepiece has a 50 degree 'apparent field of view':
    • Example: True Field of View = 50 / 100 = 1/2 degree
  • f/number = Objective Focal Length / Objective Diameter
    • Example: A 2000 mm focal length telescope that has 200 mm (8 inch) diameter yields a value of f/10.

Related Calculation Programming

  • javascript Field of View calculator
    // 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);
    }