Lenses in Contact
1/f = 1/f₁ + 1/f₂
Separated Lenses
1/f = 1/f₁ + 1/f₂ - d/(f₁f₂)
meters
Positive for converging, negative for diverging
meters
meters
Set to 0 for lenses in contact
Applications of Lens Combinations
Telescopes
Use a long focal length objective with a short focal length eyepiece to achieve high magnification.
Microscopes
Combine objective and eyepiece lenses with specific separation for high magnification of small objects.
Camera Lenses
Multiple elements correct aberrations and provide zoom capability through variable separation.
Achromatic Doublets
Converging and diverging lenses in contact reduce chromatic aberration while maintaining focusing power.