Why there is a sharp zone instead of one thin line
Light from a point on the subject comes in through the whole aperture and narrows to a cone. Only the focused distance meets as a point on the sensor.
A point a little nearer or farther reaches the sensor before or after that tip, so it leaves a disc. While the disc stays inside the circle of confusion, c = 0.030 mm on full frame, it still looks sharp.
Stop down and the blades pinch that cone. A narrower cone stays inside c for a longer distance, so the sharp zone gets deeper.
Aperture, distance, and the one-third myth
Aperture scales the zone in proportion to the f-number. From f/2 to f/4 the entrance pupil is cut in half. At 85 mm and 2 m the sharp zone grows from 6.4 cm to 12.7 cm.
Subject distance scales it much faster. At 50 mm f/1.8 the zone is 4.1 cm at 1.0 m and 16.9 cm at 2.0 m. Double the distance and the zone is about four times as deep.
The rule “one third in front, two thirds behind” is one particular distance, not a law. In front of the subject the zone is s minus the near limit. Behind it, the far limit minus s. That split is about one to two only when the subject sits at one third of the hyperfocal distance. At a portrait distance the split is nearly even. At the hyperfocal distance the far limit is infinity and the near limit sits near half that distance.
| Aperture | Entrance pupil | Near | Far | Total | Front / rear | Hyperfocal |
|---|---|---|---|---|---|---|
| f/1.2 | 70.8 mm | 1.981 m | 2.019 m | 3.8 cm | 49.5% (1.9 cm) / 50.5% (1.9 cm) | 200.8 m |
| f/1.4 | 60.7 mm | 1.978 m | 2.023 m | 4.5 cm | 49.4% (2.2 cm) / 50.6% (2.3 cm) | 172.1 m |
| f/1.8 | 47.2 mm | 1.972 m | 2.029 m | 5.7 cm | 49.3% (2.8 cm) / 50.7% (2.9 cm) | 133.9 m |
| f/2.8 | 30.4 mm | 1.956 m | 2.045 m | 8.9 cm | 48.9% (4.4 cm) / 51.1% (4.5 cm) | 86.10 m |
| f/4 | 21.3 mm | 1.938 m | 2.066 m | 12.7 cm | 48.4% (6.2 cm) / 51.6% (6.6 cm) | 60.29 m |
| f/5.6 | 15.2 mm | 1.915 m | 2.093 m | 17.8 cm | 47.8% (8.5 cm) / 52.2% (9.3 cm) | 43.09 m |
| f/8 | 10.6 mm | 1.881 m | 2.135 m | 25.5 cm | 46.8% (11.9 cm) / 53.2% (13.5 cm) | 30.19 m |
| Subject distance | Near | Far | Total | Front / rear | Typical framing |
|---|---|---|---|---|---|
| 0.70 m | 0.690 m | 0.710 m | 2.0 cm | 49.3% (1.0 cm) / 50.7% (1.0 cm) | Tight headshot |
| 1.00 m | 0.980 m | 1.021 m | 4.1 cm | 49.0% (2.0 cm) / 51.0% (2.1 cm) | Head and shoulders |
| 1.50 m | 1.454 m | 1.548 m | 9.4 cm | 48.4% (4.6 cm) / 51.6% (4.8 cm) | Half-body portrait |
| 2.00 m | 1.919 m | 2.088 m | 16.9 cm | 47.9% (8.1 cm) / 52.1% (8.8 cm) | Environmental portrait |
| 3.00 m | 2.820 m | 3.204 m | 38.3 cm | 46.8% (18.0 cm) / 53.2% (20.4 cm) | Full body |
| 5.00 m | 4.518 m | 5.598 m | 1.08 m | 44.7% (48.2 cm) / 55.3% (59.8 cm) | Group |
| 10.0 m | 8.233 m | 12.734 m | 4.50 m | 39.3% (1.77 m) / 60.7% (2.73 m) | Street |
Does a longer lens give less depth of field?
It depends on whether you stay where you are. A longer lens often blurs the background more. That is two different photographs, not one rule.
Stay at 2.0 m and the longer lens zooms in. A 24 mm f/2 keeps 85.7 cm sharp. A 135 mm f/2 from the same spot keeps 2.5 cm. The person is much larger in the frame, and the sharp zone collapses.
Step back so the head stays the same size and the zone around the person comes back. A 24 mm at 0.96 m and a 135 mm at 5.40 m both keep about 18.9 cm to 18.7 cm sharp. The photos still look different. The 135 mm shows a narrower slice of the background, and distant detail looks much softer. Lens compression
| Focal length | Sharp zone if you stay at 2.0 m | Distance for the same head size | Sharp zone at that size | Blur at the subject |
|---|---|---|---|---|
| 24 mm | 85.7 cm | 0.96 m | 18.9 cm | Ø 12.0 mm |
| 35 mm | 38.8 cm | 1.40 m | 18.8 cm | Ø 17.5 mm |
| 50 mm | 18.7 cm | 2.00 m | 18.7 cm | Ø 25.0 mm |
| 85 mm | 6.4 cm | 3.40 m | 18.7 cm | Ø 42.5 mm |
| 135 mm | 2.5 cm | 5.40 m | 18.7 cm | Ø 67.5 mm |
Sensor size, circle of confusion and equivalence
A smaller sensor must be enlarged more to reach the same print, so the largest disc that still looks sharp is smaller. The circle here is 0.030 mm times the sensor diagonal divided by the full-frame diagonal.
Matching a 50 mm full-frame angle means a shorter lens, by the crop factor. Focal length is squared in the formula and the circle only shrinks with the crop, so that shorter lens at the same f-number keeps more of the subject sharp, by about the crop factor. To match the angle and the depth of field, divide the f-number by the crop as well.
| Format | Size | Crop | Circle of confusion | Focal length | Depth of field | Hyperfocal |
|---|---|---|---|---|---|---|
| 1-inch | 13.2×8.8 | 2.73× | 0.0110 mm | 18.3 mm | 52.7 cm | 15.30 m |
| Micro Four Thirds | 17.3×13 | 2.00× | 0.0150 mm | 25.0 mm | 38.2 cm | 20.86 m |
| APS-C | 23.6×15.7 | 1.53× | 0.0197 mm | 32.8 mm | 28.9 cm | 27.33 m |
| Full frame | 36×24 | 1.00× | 0.0300 mm | 50.0 mm | 18.7 cm | 41.72 m |
| Digital medium format | 43.8×32.9 | 0.79× | 0.0380 mm | 63.3 mm | 14.7 cm | 52.82 m |
| Medium format 645 | 56×41.5 | 0.62× | 0.0483 mm | 80.5 mm | 11.4 cm | 67.20 m |
| Medium format 6×7 | 70×56 | 0.48× | 0.0622 mm | 103.6 mm | 8.8 cm | 86.43 m |
| Large format 4×5 | 121×96 | 0.28× | 0.1071 mm | 178.5 mm | 4.9 cm | 148.9 m |
| Large format 8×10 | 240×190 | 0.14× | 0.2122 mm | 353.7 mm | 2.2 cm | 295.1 m |
Hyperfocal distance
Focus at the hyperfocal distance and the sharp zone runs from about half that distance out to infinity. That is as deep as the zone can be while still reaching infinity.
The table is full frame, c = 0.030 mm. At the same focal length and f-number, a smaller sensor pushes the hyperfocal distance farther out, because its circle of confusion is smaller. At 50 mm f/2 that is 41.72 m on full frame, 63.65 m on APS-C and 83.36 m on Micro Four Thirds: about 1.53 times and twice. Divide by the crop factor only in the other case, when the focal length is shortened as well so the angle of view stays the same. The sensor control above uses the exact diagonal.
The four formulas
- H = f² / (N c) + f
- Near = H s / (H + s − f)
- Far = H s / (H − s + f), or infinity once s reaches H
- Distant blur disc at the subject = f / N
| Focal length | f/1.4 | f/2 | f/2.8 | f/4 | f/5.6 | f/8 | f/11 | f/16 |
|---|---|---|---|---|---|---|---|---|
| 16 mm | 6.11 m | 4.28 m | 3.06 m | 2.15 m | 1.54 m | 1.08 m | 0.79 m | 0.55 m |
| 24 mm | 13.74 m | 9.62 m | 6.88 m | 4.82 m | 3.45 m | 2.42 m | 1.77 m | 1.22 m |
| 28 mm | 18.69 m | 13.09 m | 9.36 m | 6.56 m | 4.69 m | 3.29 m | 2.40 m | 1.66 m |
| 35 mm | 29.20 m | 20.45 m | 14.62 m | 10.24 m | 7.33 m | 5.14 m | 3.75 m | 2.59 m |
| 50 mm | 59.57 m | 41.72 m | 29.81 m | 20.88 m | 14.93 m | 10.47 m | 7.63 m | 5.26 m |
| 85 mm | 172.1 m | 120.5 m | 86.10 m | 60.29 m | 43.09 m | 30.19 m | 21.98 m | 15.14 m |
| 135 mm | 434.1 m | 303.9 m | 217.1 m | 152.0 m | 108.6 m | 76.07 m | 55.36 m | 38.10 m |
| 200 mm | 952.6 m | 666.9 m | 476.4 m | 333.5 m | 238.3 m | 166.9 m | 121.4 m | 83.53 m |
See also Bokeh, Lens compression and How the portrait view measures the zone.
Questions
Which circle of confusion is used?
Standard viewing uses 0.030 mm on full frame, the usual limit for a print or a photo on a screen. 12 MP, 24 MP and 48 MP use one pixel of a 3:2 picture: 0.0085 mm, 0.006 mm and 0.0042 mm. The circle in use is 0.030 mm. Other sensors scale it with the diagonal.
Is depth of field always one third in front and two thirds behind?
No. That split happens when the subject is at one third of the hyperfocal distance. At portrait distance the split is nearly even. At the hyperfocal distance the far limit is infinity and the near limit is about half the hyperfocal distance.
Does a longer focal length give less depth of field?
If you stay in the same spot, yes. The person gets larger and the sharp zone collapses. If you step back so the head stays the same size, the zone around the person stays about the same. The distant background still blurs more, because the longer lens magnifies a narrower slice of it.
What is the hyperfocal distance?
H = f² / (N c) + f. Focus there and the zone runs from about H/2 to infinity. Closer than that, infinity is no longer inside the sharp zone.
Why does APS-C show more depth of field than full frame?
The same angle of view needs a shorter lens, and the shorter lens at the same f-number keeps a deeper zone. To match both the angle and the depth of field, divide the f-number by the crop factor as well.