Understanding Compound Lens Systems
In optical engineering, a compound lens consists of two or more lenses arranged along a common axis. This configuration is used in cameras, microscopes, and telescopes to correct aberrations and achieve specific magnifications that a single lens cannot provide.
Effective Focal Length (EFL)
The Effective Focal Length is the primary value used to describe the power of a lens system. When two thin lenses are separated by a specific distance, the total power of the system is not simply the sum of their individual powers. Instead, the separation distance significantly alters how light converges or diverges.
The Formula (Gullstrand's Equation)
The calculation for the focal length of two thin lenses in air is derived from Gullstrand's equation:
- 1/feq = 1/f1 + 1/f2 - d/(f1 × f2)
Where:
- f1: Focal length of the first lens
- f2: Focal length of the second lens
- d: Distance between the two lenses
- feq: Equivalent (effective) focal length of the system
Formula:
Gullstrand's Equation:
1/feff = 1/f1 + 1/f2 - d/(f1 × f2)
Or simplified for calculation: feff = (f1 × f2) / (f1 + f2 - d)