What is a thin lens? Types and characteristics

Definition

A thin lens is a transparent optical system, bounded by two refracting surfaces (curved surfaces, most often spherical), whose thickness is negligible compared to the radii of curvature and to the distances used. It deflects light rays by refraction.

Two main families

• Converging lenses: thin edges, thick center. A beam of rays parallel to the optical axis converges after the lens to a single point.
• Diverging lenses: thick edges, thin center. A beam of parallel rays appears to originate from a point located before the lens.

Characteristic elements

Element	Symbol	Definition
Optical center	O	point of the lens crossed without deviation
Image focal point	F'	point where the rays from a beam parallel to the axis converge (or appear to diverge from)
Object focal point	F	point such that an object placed at F gives an image at infinity
Image focal length	f' = OF'	algebraic quantity characterizing the lens
Vergence	C = 1/f'	expressed in diopters (denoted delta), with f' in meters

Example

A converging lens has a focal length f' = 20 cm = 0.2 m. Its vergence is C = 1/0.2 = 5 delta. For a diverging lens, f' is negative (for example f' = -20 cm), so C = -5 delta.

Classic pitfall

Do not confuse the object focal point F with the image focal point F': for a converging lens, F is located before the lens (on the incident light side) and is the mirror image of F' with respect to the optical center O. For a diverging lens, it's the opposite: F' is located before the lens.