Thin Lens Equation Image Distance, Diopters & Magnification Calculator

Solve the Gaussian thin-lens equation for real/virtual image distance and magnification.

Image Focal Distance (d_i)
62.5 mm
Lateral Magnification (M) -0.25 ×
Image Height 6 mm
Optical Power in Diopters 20 D
Inputs
mm
Lens focal length (f) in millimeters (+ converging, − diverging).
mm
Object distance from optical center (d_o) in millimeters.
mm
Physical object height in millimeters.
Results & Graph
Image Focal Distance (d_i)
62.5 mm
Lateral Magnification (M)
-0.25 ×
Image Height
6 mm
Optical Power in Diopters
20 D

Image Focal Distance (d_i)

Graph 1 • Focal Length Mm Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 mm 57.9 mm 115.7 mm 50%: 27.78 mm 27.8 50% 75%: 44.12 mm 44.1 75% 100%: 62.5 mm 62.5 100% 125%: 83.33 mm 83.3 125% 150%: 107.14 mm 107.1 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Image Focal Distance (d_i) 62.5 mm Lateral Magnification (M) -0.25 × Image Height 6 mm Optical Power in Diopters 20 D
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Image Focal Distance (d_i)62.5 mmLateral Magnification (M)-0.25 ×Image Height6 mmOptical Power in Diopters20 D
Summary: With f=50 mm and object at 250 mm, image forms at d_i = 62.5 mm (Real image) with magnification -0.25×.
Summary: With f=50 mm and object at 250 mm, image forms at d_i = 62.5 mm (Real image) with magnification -0.25×.
⚡ Send result to: Scientific →Ohm's Law & Voltage Drop →Molarity, HP & Dew Point →
Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Thin Lens & Magnification Physics & Engineering Equation

1 / f = 1 / do + 1 / di ⇒ di = f × dodo − f
M = −di / do
1 / f = 1 / d_o + 1 / d_i ⇒ d_i = (f × d_o) / (d_o − f); M = −d_i / d_o
  • focalLengthMm: Focal Length Mm (mm)
  • objectDistanceMm: Object Distance Mm (mm)
  • objectHeightMm: Object Height Mm (mm)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Thin Lens & Magnification

Solve the Gaussian thin-lens equation for real/virtual image distance and magnification.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: 1 / f = 1 / d_o + 1 / d_i ⇒ d_i = (f × d_o) / (d_o − f); M = −d_i / d_o.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Thin Lens & Magnification via 1 / f = 1 / d_o + 1 / d_i ⇒ d_i = (f × d_o) / (d_o − f); M = −d_i / d_o.

Frequently Asked Questions

What equation powers the Thin Lens Equation Image Distance, Diopters & Magnification Calculator?

It evaluates 1 / f = 1 / d_o + 1 / d_i ⇒ d_i = (f × d_o) / (d_o − f); M = −d_i / d_o using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Optics, Photonics & Acoustics

Thin Lens Equation Image Distance, Diopters & Magnification Calculator: inputs, method, and how to read the result

Solve the Gaussian thin-lens equation for real/virtual image distance and magnification.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Focal Length Mm: Lens focal length (f) in millimeters (+ converging, − diverging).
  • Object Distance Mm: Object distance from optical center (d_o) in millimeters.
  • Object Height Mm: Physical object height in millimeters.

What the calculation includes

With the default values shown, Image Focal Distance (d_i) is 62.5 mm. The calculation follows Thin Lens & Magnification Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Focal Length Mm from 50 mm to 55 mm changes Image Focal Distance (d_i) from 62.5 mm to 70.51 mm. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Science & Engineering: Scientific Calculator, Ohm's Law, Wire Voltage Drop & Resistor Series/Parallel Calculator, Molarity, Density, Engine Horsepower & Dew Point / Weather Calculator.