Optics Glossary

Comprehensive definitions of optical terms and concepts used in lens design and the lens maker formula.

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Focal Length (f)

Core Concepts

The distance from the optical center of a lens to the focal point, where parallel rays of light converge (or appear to diverge from). Measured in meters or centimeters.

Formula / Notation:

Calculated using: 1/f = (n-1)(1/R₁ - 1/Rβ‚‚)

Related Terms:

Focal PointPrincipal AxisOptical Center

Refractive Index (n)

Core Concepts

A dimensionless number that describes how fast light travels through a material compared to vacuum. Higher values indicate slower light propagation. For air, n β‰ˆ 1.00; for glass, n typically ranges from 1.4 to 1.9.

Formula / Notation:

n = c / v (speed of light in vacuum / speed in material)

Related Terms:

Snell's LawDispersionCritical Angle

Radius of Curvature (R)

Core Concepts

The radius of the sphere from which a lens surface is a portion. A larger radius means a flatter surface. The sign indicates the direction of curvature relative to the light source.

Formula / Notation:

R > 0: center on right; R < 0: center on left

Related Terms:

CurvatureSpherical SurfaceSign Convention

Converging Lens

Lens Types

A lens that causes parallel light rays to converge to a focal point. Has a positive focal length. Thicker in the middle than at the edges (e.g., biconvex lens).

Formula / Notation:

f > 0

Related Terms:

BiconvexReal ImageMagnification

Diverging Lens

Lens Types

A lens that causes parallel light rays to spread apart, appearing to originate from a virtual focal point. Has a negative focal length. Thinner in the middle than at the edges (e.g., biconcave lens).

Formula / Notation:

f < 0

Related Terms:

BiconcaveVirtual ImageReduction

Thin Lens

Lens Types

A lens whose thickness is negligible compared to its radii of curvature and focal length. The lens maker formula applies directly to thin lenses without thickness correction.

Formula / Notation:

Thickness << R₁, Rβ‚‚, f

Related Terms:

Thick LensParaxial ApproximationLens Maker Formula

Thick Lens

Lens Types

A lens where thickness significantly affects optical properties. Requires additional terms in the lens maker formula to account for the optical path through the lens material.

Formula / Notation:

1/f = (n-1)[1/R₁ - 1/Rβ‚‚ + (n-1)d/(nR₁Rβ‚‚)]

Related Terms:

Principal PlanesNodal PointsEffective Focal Length

Biconvex Lens

Lens Types

A lens with both surfaces curving outward (convex). The most common type of converging lens, used in magnifying glasses and many optical instruments.

Formula / Notation:

R₁ > 0, Rβ‚‚ < 0

Related Terms:

Converging LensDouble ConvexPositive Lens

Biconcave Lens

Lens Types

A lens with both surfaces curving inward (concave). A common diverging lens used in eyeglasses for nearsightedness and beam expanders.

Formula / Notation:

R₁ < 0, Rβ‚‚ > 0

Related Terms:

Diverging LensDouble ConcaveNegative Lens

Plano-Convex Lens

Lens Types

A lens with one flat (plano) surface and one convex surface. A simple converging lens often used in focusing applications.

Formula / Notation:

R₁ > 0, Rβ‚‚ = ∞ (or R₁ = ∞, Rβ‚‚ < 0)

Related Terms:

Converging LensAsymmetric LensCollimation

Meniscus Lens

Lens Types

A lens where both surfaces curve in the same direction, but with different radii. Can be either converging or diverging depending on the relative radii.

Formula / Notation:

Both R₁ and Rβ‚‚ have same sign

Related Terms:

Converging MeniscusDiverging MeniscusCorrective Lens

Focal Point (Focus)

Optical Geometry

The point on the principal axis where parallel rays of light converge (real focus) or appear to diverge from (virtual focus) after passing through the lens.

Formula / Notation:

Located at distance f from optical center

Related Terms:

Principal FocusFocal LengthFocal Plane

Principal Axis

Optical Geometry

An imaginary line passing through the centers of curvature of both lens surfaces. Light rays along this axis pass through without bending.

Formula / Notation:

Connects C₁ and Cβ‚‚

Related Terms:

Optical AxisOptical CenterParaxial Rays

Optical Center

Optical Geometry

The point on the principal axis through which light rays pass without deviation. For a thin lens, it is at the geometric center of the lens.

Formula / Notation:

Center of thin lens

Related Terms:

Principal AxisNodal PointLens Center

Snell's Law

Physical Laws

The fundamental law of refraction relating the angles of incidence and refraction to the refractive indices of two media. Forms the basis for deriving the lens maker formula.

Formula / Notation:

n₁ sin(θ₁) = nβ‚‚ sin(ΞΈβ‚‚)

Related Terms:

RefractionRefractive IndexCritical Angle

Lens Power (Diopter)

Measurements

The reciprocal of the focal length measured in meters. Expressed in diopters (D). A 0.5 m focal length lens has a power of 2 D.

Formula / Notation:

P = 1/f (when f is in meters)

Related Terms:

Focal LengthOptometryVision Correction

Magnification

Measurements

The ratio of image size to object size. Can be lateral (height ratio) or angular (angle ratio). Positive for upright images, negative for inverted.

Formula / Notation:

m = -s'/s = h'/h

Related Terms:

Image FormationObject DistanceImage Distance

Sign Convention

Conventions

A set of rules for assigning positive or negative values to optical quantities. The Cartesian convention measures all distances from the optical center, with positive to the right.

Formula / Notation:

Light travels left β†’ right; R > 0 if center is right of surface

Related Terms:

Cartesian ConventionReal/VirtualImage Formation

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