1 The idea
A camera is a dark box with a small hole. Light from the scene passes the hole and lands on the sensor behind it. The hole-to-sensor distance is the focal length; the image lands upside down, and the sensor’s rectangle sets how wide you see (FOV).
There are two similar triangles: sensor ÷ focal = frame at the robot ÷ distance. Raise the focal length and the sensor sits further back, so the cone narrows. A smaller sensor narrows it too (crop factor). If your phone has a tilt sensor, press the button and aim the camera by tilting it.
FOV = 2 · atan(sensor ÷ (2 · focal)) · sensor ÷ focal = frame ÷ distance2 Hands-on
No task here. Switch sensors, then change the focal length until the small camera view looks the same again.
3 Deep dive
A camera is a pinhole and a sensor
In 3D software the camera is an ideal pinhole: every ray passes one point and lands on a sensor one focal length behind it. No depth of field, no distortion, until you add them.
The pyramid from the hole out through the sensor’s edges (mirrored) is the frustum: everything inside it is in the picture, and nothing outside is rendered.
Two similar triangles
Behind the hole: half the sensor and the focal length. In front: half the frame and the distance. Same angle, so sensor ÷ focal = frame ÷ distance, and FOV = 2·atan(sensor ÷ 2·focal).
| focal | hFOV on 36 mm | frame width at 6 m |
|---|---|---|
| 18 mm | 90.0° | 12.0 m |
| 35 mm | 54.4° | 6.17 m |
| 50 mm | 39.6° | 4.32 m |
| 135 mm | 15.2° | 1.60 m |
Crop factor
Crop factor = full-frame width ÷ sensor width. Super 35 at 24.89 mm → crop ≈ 1.45; Micro 4/3 at 17.3 mm → crop ≈ 2.08. A 35 mm lens on Super 35 gives about the angle of a 50 mm on full frame, but the lens is still 35 mm.
For VFX the number you need is the sensor area actually recorded in the shooting mode (many cameras crop at some resolutions), not the sensor’s marketing name.
A focal length means nothing without its sensor size
Pan and tilt from the god view
Pan swings the cone around the vertical axis and tilt around the horizontal one. The camera doesn’t move, so the small view just slides; near and far don’t separate (lesson CL6). Phone tilt in this room drives only these two axes.
4 In real work
In Nuke
- Camera: focal length, horizontal aperture and vertical aperture are this lesson’s triangles; the apertures are the sensor size in mm.
- Viewer 3D (Tab): the camera’s frustum is drawn as lines; use it to see where the camera points and how wide it sees.
- Camera: near and far clipping set the frustum’s front and back; anything outside disappears from the render.
- The ScanlineRender format should share the aspect of horizontal ÷ vertical aperture, or the picture stretches or crops.
Common mistakes → the fix
- ✗ Using the on-set focal with the default aperture✓ Enter the sensor size of the real camera and shooting mode.
- ✗ Thinking crop factor changes the lens’s focal length✓ The lens is unchanged; the sensor just records less of the image.
- ✗ A render format that doesn’t match the aperture ratio✓ Make the format aspect = horizontal ÷ vertical aperture.
Before you send the shot
- Focal and sensor size come from the same source
- Aperture ratio matches the plate format
- Near/far clipping doesn’t cut anything you need
- Look in 3D that the camera sits and points where it should
5 Check yourself
You switch from full frame to Super 35 (crop about ×1.45) and keep 35 mm. What happens?
🔒 Answer the question above and this card opens
1. A 36 mm wide sensor with a 36 mm lens: what is the hFOV?
2. You want the angle of a 50 mm on full frame, but on Micro 4/3 (crop ≈ 2.08). Which focal?
Where the numbers come from: Sensor widths: full frame 36 mm, Super 35 24.89 mm, Micro 4/3 17.3 mm, all cropped to 16:9. The sensor is drawn 25× larger so you can see it. Phone tilt is optional and only drives pan/tilt. The camera is an ideal pinhole (no lens distortion) with a 36 mm wide sensor cropped to 16:9 (36 × 20.25 mm). The set and robot are built in code with three.js.