The Effective Focal Length Calculator helps users determine the actual focal length of a single lens or a system of lenses. In photography, microscopy, telescope optics, and other fields involving light or image focusing, it is essential to know how lenses interact.
This tool is part of the Optics and Imaging Calculators category. It allows users to compute how focal lengths combine, especially when two or more lenses are placed together. Knowing the effective focal length (EFL) is vital for understanding image size, magnification, and field of view.
Whether you're designing a custom lens system or evaluating optical performance, this calculator provides a fast and accurate way to get the values you need.
formula
For a single lens or simple optical system:
EFL = f
For a compound lens system (two lenses):
1 / EFL = 1 / f1 + 1 / f2 - d / (f1 * f2)
Variables:
EFL (Effective Focal Length):
The total or net focal length of the optical system, usually expressed in millimeters (mm) or centimeters (cm). It represents how strongly the system converges or diverges light.
f:
The focal length of a single lens.
f1, f2:
The focal lengths of the first and second lenses in the system.
d:
The physical distance between the two lenses.
This formula is especially useful when working with multi-lens setups like telescope eyepieces, camera attachments, or microscope systems.
Reference Table for Common Lens Setups
| Setup Description | f1 (mm) | f2 (mm) | d (mm) | Effective Focal Length (mm) |
|---|---|---|---|---|
| Two identical lenses close | 100 | 100 | 5 | 50.25 |
| Telephoto setup | 150 | -50 | 30 | 123.33 |
| Compound magnifying lens | 75 | 50 | 10 | 29.58 |
| Close-coupled lenses | 80 | 60 | 5 | 32.59 |
| Single lens only | 85 | — | — | 85 |
This table gives practical examples of real-world combinations, useful for quick reference when designing or comparing lens systems.
Example
Problem:
You have two lenses:
- f1 = 120 mm
- f2 = 80 mm
- Distance between lenses (d) = 10 mm
Step 1: Plug values into the formula
1 / EFL = 1 / 120 + 1 / 80 - 10 / (120 * 80)
1 / EFL = 0.00833 + 0.0125 - 0.00104 = 0.01979
EFL = 1 / 0.01979 ≈ 50.52 mm
Result:
The effective focal length of this lens system is approximately 50.52 mm.
Most Common FAQs
A: A shorter EFL usually results in a wider field of view and greater magnification in close-range imaging. It also increases image brightness in systems like telescopes.
A: Yes, when using diverging (concave) lenses or certain combinations of lenses, the EFL can be negative, indicating the system spreads light instead of focusing it.
A: The distance (d) affects how the lenses interact. Even a small change in spacing can significantly alter the EFL, especially in compact or high-precision systems.