Calculations with Optical Instruments
Conversion of Focal Lengths
Camera lenses have a focal length. Put simply, this describes the distance between the lens's principal optical plane and the focal point, but only when focused at infinity. A longer focal length results in a smaller angle of view, making objects appear larger in the image. Shorter focal lengths are typical for wide-angle shots. However, there are two different focal length specifications. These can be found in the EXIF data of digital photos, although programs for reading this data often only display one of them. If this is the case, it is usually the true, i.e., the physical focal length. Both focal lengths can be converted using the sensor size.
Please specify either the sensor diagonal or the crop factor, as well as one of the two focal lengths. The other value will be calculated. The effective focal length is also often referred to as the 35 mm equivalent focal length.
The formulas for the calculation are:
Crop factor = 43.27 millimeters / sensor diagonal
Effective focal length = Crop factor * Actual focal length
43.27 millimeters is the length of the diagonal of a full-frame sensor.
The smaller the sensor, the smaller the angle of view for the same physical focal length. Therefore, the effective focal length is converted to full-frame or 35mm equivalent. The effective focal length is thus different from the true focal length, unless the camera is full-frame. It can be shorter or longer. The effective focal length is also the one usually stated in the product description.
An important additional aspect is that the crop factor changes the angle of view, but not the physical properties of the lens itself. The true focal length always remains constant, regardless of which camera the lens is used on. However, the smaller sensor only uses a correspondingly smaller portion of the image circle projected by the lens. This creates the impression of greater magnification. The effective focal length facilitates comparison between different camera systems. Furthermore, in addition to the angle of view, the sensor size also influences other characteristics such as the achievable background blur and the perceived distance in the image, which is relevant when comparing compact cameras, bridge cameras, and full-frame cameras.
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