Camera Basics: Angle of View, Field of View and Depth of Field
What a 50mm lens shows, or how much an f/1.8 portrait blurs the background, can be worked out before you shoot. Four numbers do most of the work: focal length, sensor size, subject distance and f-number. Here is how they combine, with worked examples.
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Focal length and angle of view
Focused at infinity, angle of view = 2 × arctan(sensor dimension ÷ (2 × focal length)). Use the sensor width for horizontal, height for vertical and diagonal for the diagonal angle, which is what lens specifications usually quote.
On a full-frame 36×24mm sensor, the diagonal angle is about 84° at 24mm, 63° at 35mm, 47° at 50mm and 29° at 85mm. Doubling focal length does not quite halve the angle, and small changes matter most at the wide end. A 50mm lens covers about 40° horizontally and 27° vertically, so turning the camera upright changes what fits across the frame.
Sensor size and equivalent focal length
A smaller sensor sees less through the same lens. The crop factor, the ratio of full-frame diagonal to the sensor's diagonal, converts a focal length to its full-frame equivalent: about 1.53 for APS-C (23.5×15.6mm), 1.61 for Canon APS-C, 2.0 for Micro Four Thirds and 2.7 for 1-inch sensors. A 33mm lens on APS-C behaves like about 51mm on full frame.
Aspect ratio still matters. Micro Four Thirds is 4:3 rather than 3:2, so at the same equivalent focal length it shows slightly less width and slightly more height. Treat equivalent focal length as a guide to angle, not an exact match.
What fits in the frame
For distant subjects, the area covered is roughly sensor dimension × distance ÷ focal length. An 85mm lens on full frame at 3m covers about 1.2m × 0.8m, or 0.8m × 1.2m in portrait orientation, a comfortable head-and-torso portrait. For a group shot, 24mm at 5m covers about 7.4m × 5.0m, while 35mm at the same distance covers only about 5.1m × 3.4m.
Up close, the simple ratio overestimates. Focusing near moves the lens forward, so the thin-lens equation (1/f = 1/object distance + 1/image distance) gives a better answer: a 50mm lens on full frame at 0.5m covers about 28cm across, not the 36cm the ratio suggests. Distance here is measured from the sensor plane, as on a lens's focus scale.
What controls depth of field
Depth of field is the range that looks acceptably sharp. The threshold is the circle of confusion, commonly about 0.03mm for full frame (about 1/1500 of the diagonal) and 0.02mm for APS-C. Depth grows with a larger f-number, a shorter focal length and a greater distance.
With an 85mm f/1.8 on full frame focused at 2m, depth of field runs from about 1.97m to 2.03m, roughly 6cm, enough for one eye to be sharp and the other not. Stopping down to f/4 gives about 13cm, and moving back to 3m at f/1.8 also gives about 13cm. A 50mm f/1.8 at 2m gives about 17cm.
Hyperfocal distance for front-to-back sharpness
Hyperfocal distance, f² ÷ (N × c) + f, is the focus point at which depth of field just reaches infinity; everything from about half that distance to infinity is acceptably sharp. For 24mm at f/8 on full frame it is about 2.4m, giving sharpness from about 1.2m to infinity.
The same idea helps with group photos. At 24mm f/8 focused on a row 5m away, the sharp zone runs from about 1.6m to infinity. At 35mm f/8 focused at 5m, it runs from about 2.5m to around 180m, plenty for several rows.
Sensor size, blur and print size
At the same framing, f-number and distance, a smaller sensor gives more depth of field. An APS-C 56mm f/1.8 (about 86mm equivalent) at 2m, with a 0.02mm circle of confusion, has about 9cm of depth versus about 6cm for 85mm f/1.8 on full frame, which is why full frame is said to blur backgrounds more easily.
The circle of confusion depends on how large the photo will be viewed, so use a smaller value if you plan big prints. For printing at 300 dpi, an L-size print (89×127mm) needs 1051×1500 pixels, about 1.6 megapixels; A4 needs 2480×3508, about 8.7 megapixels; and A3 about 17.4 megapixels.