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Combined Lens Power Calculator

Work out combined lens power instantly with clear inputs, formula shown and shareable results.

About Combined Lens Power Calculator

Two thin lenses separated by a distance d combine as P = P1 + P2 - d.P1.P2. In contact the powers simply add, but separation always reduces the total for two positive lenses: +5 D and +3 D at 50 mm give 7.25 D rather than 8 D. This is the basis of every compound lens design.

Formulas

Gullstrand equation

P = P1 + P2 - d P1 P2

In contact

P = P1 + P2 when d = 0

Worked example

With the default values below, Combined Lens Power Calculator returns Combined Power of 7.2500. Change any input above and every figure here is recalculated in your browser.

Inputs used

Power of the first lens
5 D
Power of the second lens
3 D
Separation between the lensesminimum 0 m
0.05 m

Results

Combined Power
7.2500 D
Equivalent Focal Length
0.13793 m
Power If The Lenses Touched
8.000 D
Power Lost To Separation
0.7500 D

Step by step

  1. 1Values used
  2. 2Gullstrand equation
  3. 3In contact
  4. 4Combined Power= 7.2500 D
  5. 5Equivalent Focal Length= 0.13793 m
  6. 6Power If The Lenses Touched= 8.000 D
  7. 7Power Lost To Separation= 0.7500 D

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does separation reduce the power?

Because the second lens intercepts light that the first has already begun to converge, so it acts on a narrower beam and contributes less.

Can two positive lenses combine to zero power?

Yes, when d = 1/P1 + 1/P2. That afocal arrangement is exactly how a telescope's objective and eyepiece are set.

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