gen-define-focal-length-and-field-of-view-and-give-one-short-wor-c0a7

Define focal length and field of view and give one short worked example.

# Focal Length and Field of View ## Definitions **Focal Length (f)**: The distance from the optical center of a lens to the point where parallel light rays converge to a focus. Measured in millimeters (mm) for cameras. - Shorter focal length → wider view - Longer focal length → narrower, more magnified view **Field of View (FOV)**: The angular extent of the observable scene captured by a lens, typically measured in degrees. - Wider FOV → more of the scene visible - Narrower FOV → more zoomed in, less visible ## Relationship For a camera with sensor dimension *d* and focal length *f*: **FOV = 2 × arctan(d / 2f)** ## Worked Example **Problem**: A camera has a 36 mm wide sensor and uses a 50 mm lens. What is the horizontal field of view? **Solution**: - Sensor width (d) = 36 mm - Focal length (f) = 50 mm FOV = 2 × arctan(36 / (2 × 50)) FOV = 2 × arctan(36 / 100) FOV = 2 × arctan(0.36) FOV = 2 × 19.8° **FOV = 39.6°** This is considered a "normal" field of view, similar to human vision, which is why 50mm is called a "standard" lens for full-frame cameras.