Clarifying Focal Length Multiplier Confusion


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Those of you who have bought digital SLR cameras like the Canon Digital Rebel or Nikon D70 have become familiar with the industry buzzword "focal length multiplier". The common perception is that when you attach lenses made for 35mm cameras onto digital SLR backs with smaller sensors the focal length (distance between the lens center and the film) actually increases or multiplies, providing the same perspective of a longer lens on a 35mm. But is this really the case?

A quick interview with Richard Linke, Optical Society of America's director of science policy, clarified this oft-misunderstood concept and helped shed some light on the relationships between the 35mm world and the nonstandardized world of digital photography.

SK: Camera companies talk about a focal length multiplier with regard to the smaller sensor sizes of digital cameras. Does a camera's sensor size have any bearing on focal length? If not, then what are they talking about?

RL: This confusion results from the fact that we've gotten used to a single film size (namely 35mm). In the "good old days" of photography there were various film sizes -- from 16mm and smaller up to 8x10 inches (think Ansel Adams).

Photographers were comfortable with the idea that the "normal" lens for each format was different. We tend to think of a 50mm focal length lens as the "normal" lens for a 35mm camera but a camera that uses a 5x7 inch negative would use a 180mm lens as it's normal lens. So it's no surprise that a digital camera with a sensor which is typically smaller than the film plane aperture in a 35mm camera (24x36mm) would need a different focal length "normal" lens.

So what is a normal lens, anyway? Good question. The usual definition is that it is one that makes a picture with roughly the same perspective as what you see with your eyes. The eye's field of view is roughly a 45 degree spread in angle (though peripheral vision gives you more than that but it's not clear). A lens with a focal length equal to the diagonal dimension of the film (or sensor) will give you this same angular spread. A longer focal length will give you a smaller field of view so we call that a "telephoto" lens and a shorter focal length would give you more of the scene so we call that a "wide angle" lens.

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The film and digital sensor are the exact same distance from the lens, but because the sensor is smaller it captures less of the image.

SK: So, if you take a 50mm lens made for a 35mm SLR camera and put it on a digital SLR camera with a 22.7 x 15.1mm sensor (Canon Digital Rebel), you're really getting the angle of view equivalent to an 80mm lens?

RL: You're right. The 50mm with the smaller sensor would give a perspective like an 80mm with a [35mm] film camera.

SK: But does this really make the 50mm lens an 80mm telephoto lens on the digital camera?

RL: Well, imagine you take your 35mm camera and instead of putting in 35mm film you put in 16mm film, now you're only using a small part of the lens. It's just throwing away all the rest of the image.

SK: So you're getting the smaller field of view only because you're lopping off the outsides of the image?

RL: Exactly. You're just lopping off the outsides. So how can that possibly be viewed as a positive thing? And remember, for smaller sensors you will need a lens with a smaller focal length to get that "normal" field of view.

SK: So the distance between the lens and the sensor doesn't really change just because the sensor size, whether film or digital, is different?

RL: No. The focal length is exactly the distance between the lens and the film plane. So, if you have a 50mm lens, the distance between the center of that lens and the film is 50mm. If you replace the film with a sensor, that's where you have to put the sensor -- 50mm away from the lens.

After finishing my conversation with Mr. Linke, I immediately had questions about how this affects actual image quality and what other photographic factors contribute to image quality.

I realized because many digital image sensors are smaller than 35mm film, the digital image would need to be enlarged to equal a 35mm print with the same field of view. But will enlarging a digital image reduce the quality of the print? I'm not sure. Perhaps this question and other questions about image quality will be addressed in a future blog entry. Stay tuned ...

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