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Thin Lens and Mirror Calculator

Find image distance and magnification for a paraxial thin lens or spherical mirror with an explicit sign convention.

Thin Lens and Mirror Calculator

Result0.15 m

Model and interpretation

Paraxial model: 1/f = 1/dₒ + 1/dᵢ and m = −dᵢ/dₒ. Real distances are positive; converging lenses and concave mirrors have positive f. A real lens image is on the opposite side from the object; a real mirror image is in front of the mirror. At focus there is no finite image. Thick-lens and aberration effects are excluded. Real image; Inverted. 10⁻¹² ≤ |f|,dₒ,hₒ ≤ 10¹².

dᵢ (m)
0.15
m
-0.5
hᵢ (m)
-0.01

Method source: OpenStax University Physics Volume 3 — Thin LensesReport a correction

What this calculator answers

Thin Lens and Mirror Calculator applies the registered method “1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ; hᵢ = mhₒ” to the displayed Optical system, Signed focal length (m), Object distance (m), Object height (m) inputs. Both worked examples come from the production calculation engine, and OpenStax University Physics Volume 3 — Thin Lenses defines the cited method or convention; no hidden inputs or current external data are inferred.

Variables, defaults, and limits

Optical system
Optical system is a choice input. The displayed starter value is Thin lens; it is an example, not a hidden assumption.
Default: Thin lens
Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result. Available choices: Thin lens, Spherical mirror.
Signed focal length (m)
Signed focal length (m) is a number input. The displayed starter value is 0.1; it is an example, not a hidden assumption.
Default: 0.1
Accepted values: Allowed range: -1,000,000,000,000 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Object distance (m)
Object distance (m) is a number input. The displayed starter value is 0.3; it is an example, not a hidden assumption.
Default: 0.3
Accepted values: Allowed range: 0.000000000001 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Object height (m)
Object height (m) is a number input. The displayed starter value is 0.02; it is an example, not a hidden assumption.
Default: 0.02
Accepted values: Allowed range: 0.000000000001 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.

Formula and calculation rule

R[thin-lens-calculator]=1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ; hᵢ = mhₒ; x₁=Optical system; x₂=Signed focal length (m); x₃=Object distance (m); x₄=Object height (m)

Thin Lens and Mirror Calculator evaluates the registered expression “R[thin-lens-calculator]=1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ; hᵢ = mhₒ; x₁=Optical system; x₂=Signed focal length (m); x₃=Object distance (m); x₄=Object height (m)” with the validated inputs. Full calculation precision is retained until the result is formatted for display.

Worked examples

Thin Lens and Mirror Calculator evaluated example 1

Use the page’s labelled starter inputs to verify Thin Lens and Mirror Calculator.

Inputs
  • Optical system: Thin lens
  • Signed focal length (m): 0.1
  • Object distance (m): 0.3
  • Object height (m): 0.02

Evaluated result: 0.15 m

Thin Lens and Mirror Calculator evaluated example 2

Change one valid input or choice and evaluate Thin Lens and Mirror Calculator again to check that the result responds deterministically.

Inputs
  • Optical system: Thin lens
  • Signed focal length (m): -0.1
  • Object distance (m): 0.3
  • Object height (m): 0.02

Evaluated result: -0.075 m

Assumptions

  • Thin Lens and Mirror Calculator uses the visitor-entered values exactly as labelled; it does not retrieve private records or current rates.
  • The calculation is limited to the declared relationship: R[thin-lens-calculator]=1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ; hᵢ = mhₒ; x₁=Optical system; x₂=Signed focal length (m); x₃=Object distance (m); x₄=Object height (m).
  • Intermediate values are not rounded; display rounding is applied only at the presentation boundary.
  • The deterministic calculation runs locally and does not upload calculator inputs to the application API.
  • The model assumes the displayed units and idealized relationship; it is not a substitute for safety-critical design or professional measurement.

Validation and boundaries

  • Every visible required input must be present; a missing value is never replaced with zero.
  • NaN, positive or negative infinity, unsafe overflow, and a non-finite final result are rejected.
  • Field-specific minimums, maximums, and choices apply to Optical system, Signed focal length (m), Object distance (m), Object height (m).
  • Unit consistency and the displayed idealized model are required; unsafe or physically unsupported values are rejected.

Review and correction links

Common mistakes

  • Confirm the meaning and unit of Optical system, Signed focal length (m), Object distance (m), Object height (m) before calculating; a numerically valid value can still use the wrong convention.
  • Do not round intermediate values when checking the result, because early rounding can change the last displayed digits.
  • Changing an unstated real-world assumption does not change the calculator until the corresponding displayed input is changed.
  • Do not apply the idealized result to safety-critical hardware or structures without qualified review and measured tolerances.

Frequently asked questions

What question does Thin Lens and Mirror Calculator answer?
Find image distance and magnification for a paraxial thin lens or spherical mirror with an explicit sign convention. The implemented relationship is R[thin-lens-calculator]=1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ; hᵢ = mhₒ; x₁=Optical system; x₂=Signed focal length (m); x₃=Object distance (m); x₄=Object height (m).
Which inputs does Thin Lens and Mirror Calculator use?
It uses the visible fields Optical system, Signed focal length (m), Object distance (m), Object height (m). No hidden value is substituted for an omitted required input.
What happens when Thin Lens and Mirror Calculator receives an invalid or extreme value?
The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.
Why can Thin Lens and Mirror Calculator differ from another result?
Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.
Can I use Thin Lens and Mirror Calculator as professional advice?
No. It is an educational model and is not certified engineering or safety analysis.
How can I verify the Thin Lens and Mirror Calculator result?
Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with OpenStax University Physics Volume 3 — Thin Lenses.

Source and review scope

OpenStax University Physics Volume 3 — Thin Lenses

Scope: OpenStax University Physics Volume 3 — Thin Lenses is used to check the formula, definition, or convention relevant to Thin Lens and Mirror Calculator. The citation does not supply current personal, lender, tax, medical, or market data.

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