Focal Length

Two meanings of f

• Pinhole model: $f$ is the distance from the pinhole (camera center) to the image plane.
• Lens: $f$ is a physical property of the lens, the distance at which parallel rays converge. The perspective is set by the sensor distance $s_i$.

Gaussian lens formula

$$\frac{1}{s_o}+\frac{1}{s_i}=\frac{1}{f}$$

$s_o$: object distance, $s_i$: sensor (image) distance. For $s_o\to \infty$, $s_i\to f$: a lens with focal length $f$ is equivalent to a pinhole at distance $f$.

Field of view

$$\text{FOV}=2\arctan \left(\frac{h}{2f}\right)$$

$h$ is the sensor size. Larger focal length, narrower field of view (zoom).

Trap

Changing the focal length does not change perspective relationships. Only moving the camera (the viewpoint) does. A telephoto lens lets you move back while keeping the subject size, and that is what makes the background look bigger.

Appears in

• Lecture 2.1, The Gaussian Lens Formula
• Lecture 2.1, Focal Length, Field of View and Viewpoint
• Lecture 2.1, Intrinsic parameters: $f/s_x$, $f/s_y$

Related concepts

• Pinhole Camera Model
• Intrinsic Parameters
• Orthographic Projection