Optical Magnification Calculator: equations, variables, units and worked solution

The optical magnification calculator calculates Linear magnification from Image Distance, Object Distance. 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 Optical Magnification Calculator, Image Distance and Object Distance are normalized to m and m before -imageDistance/objectDistance is evaluated. The unrounded value used for Linear magnification is retained internally; formatting is applied only to the result cards.

Formula model

Governing equation: -imageDistance/objectDistance.

Formula-based worked derivation

1. Linear magnification
   1. Formula: Linear magnification = -imageDistance ÷ objectDistance
   2. Default substitution: Linear magnification = -(0.15) ÷ (0.3)
   3. Unrounded evaluation: -0.5 ×
   4. Displayed answer: -0.5 ×

In the Optical Magnification Calculator, changing Image Distance and Object Distance rebuilds the numeric substitution for -imageDistance/objectDistance. The engine converts selected measurements to m and m, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify Linear magnification with a numerical residual.

Input and output interpretation

Use measured or documented values for Image Distance, Object Distance. The calculated outputs are Linear magnification. 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 Optical Magnification Calculator uses its own `optical-magnification` JavaScript engine to calculate Linear magnification from Image Distance and Object Distance with -imageDistance/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 `optical-magnification` engine is rejected.

Visual interpretation

In the Optical Magnification Calculator, this guidance applies to Image Distance and Object Distance and the reported Linear magnification. The `optical-magnification` workflow evaluates -imageDistance/objectDistance in m and m; Confirm sign conventions, unit systems, material properties and boundary conditions before engineering use.. Verification context: dfe184.

Dimensional formula audit

The optical magnification calculator normalizes imageDistance (Image Distance, m), objectDistance (Object Distance, m) before evaluating the equations. Its reported quantities are Linear magnification in ×. 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.

• Linear magnification = -imageDistance ÷ objectDistance

Formula sensitivity and boundary verification

To verify the optical magnification calculator, hold all other inputs fixed and change imageDistance within its permitted range. The live substitution line shows exactly where that value enters the equation for Linear magnification. 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 optical magnification calculator reproducible instead of relying on an unexplained result.

Limitations

The Optical Magnification Calculator validates the supported domain for Image Distance and Object Distance before evaluating -imageDistance/objectDistance. Undefined denominators, impossible roots, non-finite values, and out-of-range selections are rejected before Linear magnification is displayed.