Thin Lens Equation Calculator

Thin Lens Equation Calculator: equations, variables, units and worked solution

The thin lens equation calculator calculates Thin Lens Equation — image distance, Lateral magnification, Thin Lens Equation — image height, Lens power from Lens focal length, Object distance, Object height. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Thin Lens Equation Calculator, Lens focal length, Object distance, and Object height are normalized to m, m, and m before 1/(1/focalLength-1/objectDistance) is evaluated. The unrounded value used for 1/(1/focalLength-1/objectDistance) and Thin Lens Equation — image distance is retained internally; formatting is applied only to the result cards.

Formula model

Thin-lens imaging uses 1/f = 1/do + 1/di, with magnification m = -di/do.

Formula-based worked derivation

1. Thin Lens Equation — image distance
   1. Formula: Thin Lens Equation — image distance = 1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)
   2. Default substitution: Thin Lens Equation — image distance = 1 ÷ (1 ÷ (0.1)-1 ÷ (0.3))
   3. Unrounded evaluation: 0.15 m
   4. Displayed answer: 0.15 m
2. Lateral magnification
   1. Formula: Lateral magnification = -(1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)) ÷ objectDistance
   2. Default substitution: Lateral magnification = -(1 ÷ (1 ÷ (0.1)-1 ÷ (0.3))) ÷ (0.3)
   3. Unrounded evaluation: -0.5 x
   4. Displayed answer: -0.5 x
3. Thin Lens Equation — image height
   1. Formula: Thin Lens Equation — image height = objectHeight × -(1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)) ÷ objectDistance
   2. Default substitution: Thin Lens Equation — image height = (0.05) × -(1 ÷ (1 ÷ (0.1)-1 ÷ (0.3))) ÷ (0.3)
   3. Unrounded evaluation: -0.025 m
   4. Displayed answer: -0.025 m
4. Lens power
   1. Formula: Lens power = 1 ÷ focalLength
   2. Default substitution: Lens power = 1 ÷ (0.1)
   3. Unrounded evaluation: 10 diopters
   4. Displayed answer: 10 diopters

In the Thin Lens Equation Calculator, changing Lens focal length, Object distance, and Object height rebuilds the numeric substitution for 1/(1/focalLength-1/objectDistance). The engine converts selected measurements to m, m, and m, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify 1/(1/focalLength-1/objectDistance) and Thin Lens Equation — image distance with a numerical residual.

Input and output interpretation

Use measured or documented values for Lens focal length, Object distance, Object height. The calculated outputs are Thin Lens Equation — image distance, Lateral magnification, Thin Lens Equation — image height, Lens power. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Thin Lens Equation Calculator uses its own `thin-lens` JavaScript engine to calculate 1/(1/focalLength-1/objectDistance) and Thin Lens Equation — image distance from Lens focal length, Object distance, and Object height with 1/(1/focalLength-1/objectDistance). Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `thin-lens` engine is rejected.

Visual interpretation

In the Thin Lens Equation Calculator, this guidance applies to Lens focal length, Object distance, and Object height and the reported 1/(1/focalLength-1/objectDistance) and Thin Lens Equation — image distance. The `thin-lens` workflow evaluates 1/(1/focalLength-1/objectDistance) in m, m, and m; Confirm sign conventions, unit systems, material properties and boundary conditions before engineering use.. Verification context: dfe184.

Dimensional formula audit

The thin lens equation calculator normalizes focalLength (Lens focal length, m), objectDistance (Object distance, m), objectHeight (Object height, m) before evaluating the equations. Its reported quantities are Thin Lens Equation — image distance in m, Lateral magnification in x, Thin Lens Equation — image height in m, Lens power in diopters. This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Thin Lens Equation — image distance = 1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)
• Lateral magnification = -(1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)) ÷ objectDistance
• Thin Lens Equation — image height = objectHeight × -(1 ÷ (1 ÷ focalLength-1 ÷ objectDistance)) ÷ objectDistance
• Lens power = 1 ÷ focalLength

Formula sensitivity and boundary verification

To verify the thin lens equation calculator, hold all other inputs fixed and change focalLength within its permitted range. The live substitution line shows exactly where that value enters the equation for Thin Lens Equation — image distance. Repeat the check with objectDistance. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the thin lens equation calculator reproducible instead of relying on an unexplained result.

Limitations

The Thin Lens Equation Calculator validates the supported domain for Lens focal length, Object distance, and Object height before evaluating 1/(1/focalLength-1/objectDistance). Undefined denominators, impossible roots, non-finite values, and out-of-range selections are rejected before 1/(1/focalLength-1/objectDistance) and Thin Lens Equation — image distance is displayed.