What are the sign conventions for lenses?

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- 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
R1R2
Biconvex
R> 0R2 < 0
Diverging MeniscusR> 0
R2 > 0
Converging Meniscus
R1 < 0
R2 < 0
BiconcaveR1 < 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:

QuantityCondition
Sign
Focal LengthConvex Lens
Concave Lens
Positive (+)
Negative (-)
Object Distance
Always
Negative (-)
Image Distance
Real Image 
Virtual Image 
Positive (+)
Negative (-)

Magnification
Upright Image
Upturn Image
Positive (+)
Negative (-)