Focal Length (f)
Core ConceptsThe 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/Rβ - 1/Rβ)
Related Terms:
Focal PointPrincipal AxisOptical Center
Refractive Index (n)
Core ConceptsA dimensionless number that describes how fast light travels through a material compared to vacuum. Higher values indicate slower light propagation. For air, n β 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 ConceptsThe 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 TypesA 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).
Related Terms:
BiconvexReal ImageMagnification
Diverging Lens
Lens TypesA 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).
Related Terms:
BiconcaveVirtual ImageReduction
Thin Lens
Lens TypesA 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 << Rβ, Rβ, f
Related Terms:
Thick LensParaxial ApproximationLens Maker Formula
Thick Lens
Lens TypesA 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/Rβ - 1/Rβ + (n-1)d/(nRβRβ)]
Related Terms:
Principal PlanesNodal PointsEffective Focal Length
Biconvex Lens
Lens TypesA lens with both surfaces curving outward (convex). The most common type of converging lens, used in magnifying glasses and many optical instruments.
Formula / Notation:
Rβ > 0, Rβ < 0
Related Terms:
Converging LensDouble ConvexPositive Lens
Biconcave Lens
Lens TypesA lens with both surfaces curving inward (concave). A common diverging lens used in eyeglasses for nearsightedness and beam expanders.
Formula / Notation:
Rβ < 0, Rβ > 0
Related Terms:
Diverging LensDouble ConcaveNegative Lens
Plano-Convex Lens
Lens TypesA lens with one flat (plano) surface and one convex surface. A simple converging lens often used in focusing applications.
Formula / Notation:
Rβ > 0, Rβ = β (or Rβ = β, Rβ < 0)
Related Terms:
Converging LensAsymmetric LensCollimation
Meniscus Lens
Lens TypesA 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 Rβ and Rβ have same sign
Related Terms:
Converging MeniscusDiverging MeniscusCorrective Lens
Focal Point (Focus)
Optical GeometryThe 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 GeometryAn imaginary line passing through the centers of curvature of both lens surfaces. Light rays along this axis pass through without bending.
Formula / Notation:
Connects Cβ and Cβ
Related Terms:
Optical AxisOptical CenterParaxial Rays
Optical Center
Optical GeometryThe 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 LawsThe 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:
nβ sin(ΞΈβ) = nβ sin(ΞΈβ)
Related Terms:
RefractionRefractive IndexCritical Angle
Lens Power (Diopter)
MeasurementsThe 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
MeasurementsThe 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
ConventionsA 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
Apply Your Knowledge
Use the calculator to practice with these concepts.