What are the Sign Conventions for Lenses?

Optical Components

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Editorial Team - GoPhotonics

Dec 6, 2022

SIGN CONVENTION FOR LENSES

A lens is a curved surface that causes the light rays falling on it to either converge or diverge. The sign convention is a set of rules that determine the signs of the parameters associated with a lens. Consider a lens having radii of curvatures as R₁ and R₂ corresponding to the surfaces S₁ and S₂ respectively.

The sign of R₁ and R₂ depends on the shape of the surfaces constituting the lens. We can say,

R₁>0 if S₁ is convex

R₁<0 if S₁ is concave

R₂>0 if S₂ is concave

R₂<0 if S₂ is convex

We can tabulate the sign convention of the radii of curvatures of the two surfaces of a lens as:

Type of Lens	R₁	R₂
Biconvex	R₁> 0	R₂< 0
Diverging Meniscus	R₁> 0	R₂> 0
Converging Meniscus	R₁ < 0	R₂< 0
Biconcave	R₁ < 0	R₂> 0
Plano-concave	R₁ = ∞	R₂> 0
Plano-convex	R₁ = ∞	R₂< 0
Plano-concave	R₁< 0	R₂ = ∞
Plano-convex	R₁ = ∞	R₂ = ∞

Lens sign convention table:

Quantity	Condition	Sign
Focal Length	Convex Lens Concave Lens	Positive (+) Negative (-)
Object Distance	Always	Negative (-)
Image Distance	Real Image Virtual Image	Positive (+) Negative (-)
Magnification	Upright Image Upturn Image	Positive (+) Negative (-)