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PhysicsSpecular and diffuse reflection

Reflection angles are measured from the local normal.

ModelPhysicsTotal internal reflection and evanescent fields

Total reflected flux does not mean zero field beyond the interface.

ModelPhysicsSpherical-mirror images and signs

A virtual image is formed by ray extensions, not actual ray convergence.

ModelPhysicsPhotoelectric threshold and stopping potential

Photon frequency sets maximum photoelectron energy in the single-photon model.

ModelPhysicsDe Broglie wavelength and particle momentum

A momentum state has a spatial wave phase.

ModelMeasurementQuantity kind and physical dimension

Equal dimensions do not make quantities interchangeable.

DefinitionMeasurementQuantity value, numerical value and unit

A numerical value depends on the chosen unit.

DefinitionMeasurementCoherent derived units

Coherence means no extra numerical factor in the base-unit product.

DefinitionMeasurementOrdinal quantities and nominal properties

Ordering and category labels do not justify ordinary arithmetic.

DefinitionMeasurementMeasurement principle, method and procedure

A physical phenomenon, an approach and a detailed procedure have different roles.

DefinitionMeasurementMeasuring instrument and measuring system

A complete measurement system can include more than one device.

DefinitionMeasurementSensor, transducer and detector

Component names describe different measurement roles.

DefinitionMeasurementInstrument indication and measurement result

A displayed reading is only one part of a measurement result.

DefinitionMeasurementAdjustment, calibration and zero adjustment

Changing an instrument response differs from determining its calibration.

DefinitionMeasurementReference and conventional quantity values

An accepted comparison value need not be an exact true value.

DefinitionMeasurementIndication interval, measuring interval and span

Possible readings differ from a validated interval of measurement.

DefinitionMeasurementRated operating conditions

Instrument properties are specified within a domain of use.

DefinitionMeasurement · ChemistrySelectivity of a measuring system

Responding to a target differs from excluding interference.

DefinitionMeasurementDiscrimination threshold and dead band

An undetected input change differs from an interval with no output change.

DefinitionMeasurementStability of a measuring instrument

Time stability differs from short-term repeatability.

DefinitionMeasurementMaximum permissible error and accuracy class

A specification limit is not an uncertainty estimate.

DefinitionMeasurementDefinitional uncertainty

More repetitions do not resolve an underspecified measurand.

DefinitionMeasurementRelative standard uncertainty

Relative uncertainty uses a nonzero measured magnitude.

DefinitionMeasurementBlank indications and null measurement uncertainty

A zero or blank reading can still have uncertainty.

DefinitionMeasurementTarget measurement uncertainty

An intended-use target differs from achieved uncertainty.

DefinitionMeasurementIntermediate precision conditions

Within-location changed conditions differ from strict repeatability.

DefinitionMeasurementCommutability of a reference material

Certification alone does not establish equivalence across procedures.

DefinitionChemistrySubstances, elements, compounds and mixtures

Chemical composition and spatial uniformity describe different features of matter.

DefinitionChemistryPhysical change and chemical change

A change of phase need not change chemical identity.

DefinitionChemistryEmpirical, molecular and structural formulas

A formula's subscripts represent different information in different chemical models.

Definition
ModelSource checked

Spherical-mirror images and signs

Physics

A virtual image is formed by ray extensions, not actual ray convergence.

Key knowledge

In paraxial spherical-mirror optics, 1/f=1/d_o+1/d_i, f=R/2 and transverse magnification m=−d_i/d_o. In the real-is-positive convention, concave f,R are positive, convex f,R negative; real images have d_i>0 and virtual images d_i<0. Negative m inverts the image. Outside the paraxial region, spherical aberration prevents one exact focus.

Values and equations

1/f=1/d_o+1/d_i; f=R/2; m=−d_i/d_o

f,R,d_o,d_i
Signed focal length, curvature radius and object/image distances m
m
Signed transverse magnification 1

Conditions and scope

  • Small ray angles and heights compared with |R|; consistent real-is-positive object/image signs and nonzero finite distances in the displayed expressions.
  • A plane mirror is the R→∞ limit and has d_i=−d_o. Other sign conventions are valid when used consistently; a virtual image does not require light to travel behind an opaque mirror.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics Volume 3, §2.2: spherical mirrorsSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §2.2 paraxial focal relation2.1, mirror equation2.6, explicit sign convention and magnification2.8. Restore paraxial scope rather than adopting prose that all parallel rays of a spherical mirror share one focus.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Related reference entries

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Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • In paraxial spherical-mirror optics, 1/f=1/d_o+1/d_i, f=R/2 and transverse magnification m=−d_i/d_o. In the real-is-positive convention, concave f,R are positive, convex f,R negative; real images have d_i>0 and virtual images d_i<0. Negative m inverts the image. Outside the paraxial region, spherical aberration prevents one exact focus.

    This relation concerns the stated spherical-mirror images and signs claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  2. Related to
    Relationship sources · 1

    Linked statements

    • In paraxial spherical-mirror optics, 1/f=1/d_o+1/d_i, f=R/2 and transverse magnification m=−d_i/d_o. In the real-is-positive convention, concave f,R are positive, convex f,R negative; real images have d_i>0 and virtual images d_i<0. Negative m inverts the image. Outside the paraxial region, spherical aberration prevents one exact focus.

    This relation concerns the stated spherical-mirror images and signs claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Uses definition
    Relationship sources · 1

    Linked statements

    • In paraxial spherical-mirror optics, 1/f=1/d_o+1/d_i, f=R/2 and transverse magnification m=−d_i/d_o. In the real-is-positive convention, concave f,R are positive, convex f,R negative; real images have d_i>0 and virtual images d_i<0. Negative m inverts the image. Outside the paraxial region, spherical aberration prevents one exact focus.

    This relation concerns the stated spherical-mirror images and signs claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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