By Zencalcy Editorial TeamLast reviewed About us
When two thin lenses touch, their powers simply add. That makes it easy to stack a corrective lens and a reading addition, or to work out what second lens is needed to bring a system to a target focal length.
Total power of thin lenses in contact.
P = P₁ + P₂ f = 1 / P
P₁ and P₂ are the individual powers in dioptres. The relation assumes the lenses are thin and in contact; separated lenses need the full system matrix.
| Symbol | Meaning |
|---|---|
| P | Combined optical power in dioptres. |
| P₁, P₂ | Powers of the individual lenses. |
| f | Equivalent focal length of the pair. |
The combined power is +5 D, giving an equivalent focal length of 0.2 m. A −1 D lens added in contact would bring it to +4 D.
Continue with the Lens Maker's Equation Calculator, Lens Power Calculator, or the Light Frequency Calculator — or browse more optics and light tools and all physics calculators.
Power is the reciprocal of focal length. Reciprocal addition is what the thin-lens combination actually does, so 1/f = 1/f₁ + 1/f₂.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026