# What are the Sign Conventions for Lenses?

#### 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 LensConcave Lens Positive (+)Negative (-) Object Distance Always Negative (-) Image Distance Real Image Virtual Image Positive (+)Negative (-) Magnification Upright ImageUpturn Image Positive (+)Negative (-)