Free · Measurement and planning

Thin Lens Distance and Extension Model

Resolve ideal thin-lens object and image distances from focal length and total subject-to-sensor distance, including a fixed-distance extension model.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked example, objectDistance = 0.2000000000, sensorDistance = 0.2000000000, magnification = 1.000000000.

For total object-to-sensor distance d, r = √(d²/4 − f d); object distance = d/2 + r; sensor distance = d/2 − r.

Worked example

Enter these known values and leave the other values blank.

Focus distance (d)
0.4 m
Focal distance (f)
100 mm
Extension tube
0 mm
Magnification
1
Object distance (g)
0.2 m
Sensor distance (h)
0.2 m

Assumptions and limitations

  • Ideal thin lens, real-image branch with d ≥ 4f. Focus distance is total object-to-sensor distance, not subject-to-lens distance.
  • Extension output uses (sensor distance + tube length)/object distance with the original object distance fixed. Refocusing a real extended lens changes these distances; this output is only the stated geometry model.
  • Results follow the stated ideal arithmetic model. Display rounding does not change the underlying calculation.
  • Supply sufficient known values and leave the desired quantity blank. Controls retain captured inverse branches and units.
  • If a retained lock prevents a reverse calculation, unlock the quantity you want to solve before supplying the known values.

Common questions

What does the worked example demonstrate?

For total object-to-sensor distance d, r = √(d²/4 − f d); object distance = d/2 + r; sensor distance = d/2 − r.

Can I change the measurement units?

Available selectors convert the entered physical quantity. Use compatible units for all related quantities.

Why can a result be blank?

A missing input, invalid denominator or underdetermined relationship cannot provide a unique finite result.

References

Use exact-sign physical domains, exact discrete counts where applicable, and documented model bounds. Source arithmetic is preserved.

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