CALCULATORS / OPTICS, IMAGING AND ILLUMINATION

Thin-lens imaging calculator

Paraxial positive thin lens with real object beyond focus.

optics-thin-lens.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	imageDistancemm	magnification
	60	-0.2
	46.1538	-0.153846

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

real image applicability300.00 mm✓ passes

BASELINE INPUTS

focal50 mmobjectDistance300 mm

CALCULATED

imageDistance60 mm

magnification-0.2

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Thin-lens imaging
# Scope: Paraxial positive thin lens with real object beyond focus.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

focal = 50 mm
objectDistance = 300 mm

imageDistance := 1/(1/focal-1/objectDistance) [mm]
magnification := -imageDistance/objectDistance

check real image applicability: objectDistance > focal

scenario alternative: focal = 40 mm

Calculated from your source · not saved

Baseline · Baseline

real image applicability300.00 mm ✓ passes

alternative · alternative

real image applicability300.00 mm ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

image distance: imageDistance = 1/(1/focal-1/objectDistance) [mm]
magnification: magnification = -imageDistance/objectDistance

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

focal: 50 mm
object distance: 300 mm

Calculated

image distance: 60 mm
magnification: -0.2

Assumptions and limits

Paraxial positive thin lens with real object beyond focus.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Thin-lens imaging. Inputs: focal length; object or image distance. Outputs: image distance; magnification. Model scope: Paraxial geometry or calibrated radiometric/photometric models. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: focal length, object or image distance
Outputs: image distance, magnification
Modes: calculate, compare, sweep
Drawing: Ray diagram and camera view

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS