Combination of lenses
Intermediate
Powers add for thin lenses in contact.
P = P₁+P₂Thin lenses in contact: P = P₁ + P₂. For separated lenses, the image from the first is the object for the second.
+3 D and −1 D: +2 D.
Don't just add focal lengths.
In more detail
Two thin lenses in contact have a combined power equal to the sum of their individual powers, P = P1 + P2. Separated lenses require a more careful calculation.
Real-world uses
- Camera lens systems combine several lenses to correct aberrations.
- Eyeglass lenses combine powers for prescriptions with astigmatism.
- Camera lenses combine several elements, and their powers add when they are placed close together.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Do powers always add?
For thin lenses in contact, yes. Separated lenses need the full lens formula.
Why combine lenses?
To achieve focal lengths and corrections that a single lens cannot provide.
Why do some camera lenses have many elements?
Each element corrects a particular aberration, so the combined lens gives sharp images across the frame.
Related topics in Optics
Lens formula · Lens maker's formula · Power of a lens · Lens aberrations · Human eye · Defects of vision