Calculating Effective Focal Length: A Comprehensive Guide
Understanding the effective focal length (EFL) of a lens system is crucial in optics and photography. The EFL is a measure that helps us determine the magnification and overall performance of a lens system, whether it involves a single lens or a complex setup with multiple lenses. This article will provide a detailed guide on calculating the EFL, along with examples and explanations.
Effective Focal Length for a Single Lens
The effective focal length for a single lens is straightforward: it is simply the focal length of the lens itself, denoted as ( f ). This is a basic starting point in any lens system analysis.
Effective Focal Length for Multiple Thin Lenses in Contact
When dealing with multiple thin lenses that are in contact, their surfaces are very close together, and the effective focal length can be calculated using the following formula:
$$frac{1}{f_{text{eff}}} frac{1}{f_1} frac{1}{f_2} frac{1}{f_3} ldots$$Here, ( f_{text{eff}} ) represents the effective focal length of the combined lens system, and ( f_1, f_2, f_3, ldots ) are the focal lengths of the individual lenses.
Effective Focal Length for Lenses Separated by a Distance
For lenses that are separated by a distance ( d ), the formula changes slightly:
$$frac{1}{f_{text{eff}}} frac{1}{f_1} frac{1}{f_2} - frac{d}{f_1 f_2}$$In this formula, ( d ) is the distance between the two lenses. This adjustment accounts for the additional optical path provided by the separation distance.
Example Calculation
Suppose you have two lenses:
Lens 1 with a focal length ( f_1 20 text{cm} )
Lens 2 with a focal length ( f_2 30 text{cm} )
They are separated by a distance ( d 5 text{cm} )
Using the formula for separated lenses:
$$frac{1}{f_{text{eff}}} frac{1}{20} frac{1}{30} - frac{5}{20 times 30}$$Calculating each term:
$$frac{1}{f_{text{eff}}} 0.05 0.0333 - 0.00833$$Then:
$$frac{1}{f_{text{eff}}} 0.075$$So, ( f_{text{eff}} frac{1}{0.075} approx 13.33 text{cm} )
The Focal Length of a Lens: Understanding and Calculation
The focal length of a lens is the distance from the rear nodal point to the image plane when the lens is focused at infinity. This concept is fundamental, but it's not something we typically calculate without a detailed diagram of the lens and its properties. The rear nodal point is not usually an actual lens element.
Zoom Lenses and Effective Focal Length
It's important to note that the effective focal length does not change unless you are dealing with a zoom lens, which can have a range of focal lengths available. The focal length at different zoom levels is the actual focal length of the lens at that zoom level, not an effective focal length.
Affecting Focal Length Without Zooming
The focal length can be adjusted without zooming by adding a teleconverter between the lens and the camera. Teleconverters usually provide a 1.4x or 2x modifier to the current focal length of the lens, effectively making it longer.
Focal Length Relative to Camera Sensor Size
When you mount a lens on a different camera, the actual focal length of the lens does not change. A 50mm lens is still a 50mm lens, whether it's mounted on an APS-C body, a full-frame body, or a medium format camera. The field of view is what changes, not the focal length.
Field of View Calculations
Field of view (FOV) is related to the focal length and the sensor size. The formula to determine FOV is:
$$FOV 2 arctan frac{x}{2f} $$Where ( x ) is the diagonal of the film or sensor and ( f ) is the focal length. As the focal length increases, the field of view decreases. However, an increase in the sensor diagonal increases the field of view. The focal length remains constant, regardless of the sensor size.
Crop Factor and Equivalence
The focal length can be related to different sensor sizes using a 'crop factor,' which is a term used to describe the relative change in field of view. The crop factor shows how a full-frame image would need to be cropped to match the field of view of a lens on a different sensor size:
Canon or Fuji APS-C: 1.6x Nikon APS-C: 1.5x Micro4/3rds: 2x Phone cameras: 6–8xFor example, a Nikon APS-C body with a 50mm lens will have the same field of view as a full-frame camera with a 75mm lens (50 * 1.5). The 50mm lens remains a 50mm lens, and the crop factor only has meaning if you are using the same lenses on different formats. If you only shoot APS-C, the full-frame equivalent is meaningless because it describes how the lens would work on a camera you don’t use.