# Focal Length Multiplier

Many digital SLRs have sensors smaller than the sensitive area of 35mm film. Typically the sensor diagonal is 1.5 times smaller than the diagonal of 35mm film.

 The FLM of a typical 6 megapixel digital SLR is 43.3/28.1 or 1.54X

As a consequence, a sensor smaller than a 35mm film frame captures only the middle portion of the information projected by the lens into the 35mm film frame area, resulting in a "cropped field of view". A 35mm film camera would require a lens with a longer focal length to achieve the same field of view. Hence the term Focal Length Multiplier (FLM). The FLM is equal to the diagonal of 35mm film (43.3mm) divided by the diagonal of the sensor. Let's now discuss two cases.

 Case 1 - Digital SLR and 35mm film camera use lenses with the same FOCAL LENGTH. Information projected by a 200mm lens onto the 35mm film frame area. The sensor with FLM of 1.5X captures only part of the information projected by the 200mm lens into the 35mm film area. This results in a "cropped field of view", equivalent to the field of view of a 200 x 1.5 = 300mm lens on a 35mm film camera (see Case 2). The absolute size of the bird projected onto the sensor is the same as on the 35mm film because the focal length is still 200mm.

A 35mm film camera would require a lens with a focal length of 300mm to achieve the same field of view, as explained in Case 2 below.

 Case 2 - Digital SLR and 35 mm film camera use lenses to achieve the same FOV. Information projected by a 300mm lens onto the 35mm film frame area. Information projected by a 200mm lens onto the sensor with FLM of 1.5X. The Field of View is the same as the 300 mm lens on the 35mm camera. The absolute size of the bird projected onto the sensor is smaller compated to the 35mm film because a lens with shorter focal length is used (different magnification).

So a 200mm lens on a digital SLR with FLM of 1.5X will have the field of view of a 300mm lens on a 35mm film camera which would be heavier and more expensive. Also, because the 35mm equivalent field of views are achieved with shorter focal lengths, depth of field is larger[1]. This advantage on the tele end becomes a disadvantage on the wide range end. For instance, a 19mm lens fitted onto a digital SLR with FLM of 1.5X will only generate the field of view of a 28mm lens fitted on a 35mm film camera.

## "Digital" SLR Lenses

Most digital SLRs are able to use conventional 35mm lenses. However, such lenses are designed to create an image circle that covers a 35mm film frame and are therefore larger and heavier than necessary for sensors which are smaller than a 35mm film frame. "Digital" lenses (e.g. Canon Short Back Focus Lenses, Nikon DX Lenses, Olympus 4/3" System) are lighter because their image circles only cover the sensor area.

## Footnote on Digital Compact Cameras

Digital compact cameras are fitted with lenses with short focal lengths to create 35mm equivalent field of views on their small sensor surfaces. Typically the sensor diagonal is 4 times smaller than the diameter of 35mm film. A 7mm lens fitted on such a camera will have the same field of view of a 7mm x 4 or 28mm lens on a 35mm film camera. Just like the digital lenses for digital SLRs, these lenses are designed to generate image circles to cover the smaller sensor. This allows these lenses to be much smaller and cheaper to manufacture Because of the very small focal lengths used, the depth of field is much larger[1] than digital SLRs or 35mm film cameras with the same field of view.

### Technical Footnotes (only relevant to advanced users)

1. (1) Assuming the aperture and subject distance remain constant, the increase in depth of field (DOF) due to the reduction in focal length is partially offset by the reduction in the maximum permissible Circle of Confusion (CoC). For a smaller format (e.g. a sensor with FLM of 1.5X is a smaller format than 35mm film), the maximum permissible CoC is smaller[2], so DOF will be smaller. However, this reduction in DOF is smaller than the increase in DOF caused by the reduction in focal length, so overall DOF will increase, and more so with larger FLMs. You can verify this by using the depth of field calculator on this site.
2. (2) In Case 2 it is easy to understand that if you print an 8" x 10" of both images, the optical information collected by the smaller sensor has to be enlarged more than the optical information collected by the 35mm film, so the maximum permissible CoC for the sensor is smaller.