# Lens Multiplication Factor Explained Once and for All

Started Mar 15, 2009 | Discussions
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Lens Multiplication Factor Explained Once and for All

When using an FX lens on a DX camera the lens manufacturers use something called a "lens multiplication factor" to describe the difference in the image when used on a DX format camera.

A 120mm FX lens has a focal length of 120mm regardless of the camera it is attached to. If mounted on a DX format camera the focal length of the lens does not magically change.

A DX sensor is smaller (15.8 x 23.6mm) than an FX sensor (23.9 x 36.0mm). When a lens designed for use on an FX sensor is used on a DX sensor some of the image falls outside the area of the sensor. Hence the image is cropped (less angle of view).

Thinking of this as a narrowing of the angle of view not an increase in focal length is a more accurate representation of the difference.

However, the image in not magnified at all, just less of the image is recorded (the angle of view is narrowed as if a long focal length lens had been used).

The image circle created by a 35mm format lens is shown.

The blue rectangle shows what a 35mm film, or a full-frame digital SLR will record.

The inner red frame shows what a digital SLR with a 1.6X magnification factor will record.

The focal length of a lens is the effective distance from the front surface of the front lens element to the focal plane of the camera. This distance can be greater than the physical distance due to the magnification factor of the lens elements used.

The magnification factor of a lens is determined by the focal length of the lens and the distance of the subject from the front surface of the lens.

In Conclusion:

When an FX format lens is mounted on a DX format camera the physical characteristics of the lens (focal length and magnification) does not changed. The only thing that changes is the amount of image that falls on the sensor.

Mounting a 120mm FX format lens on a DX format camera does not make the lens a 180mm lens.

The image used was borrowed from http://www.luminous-landscape.com/tutorials/understanding-series/dslr-mag.shtml

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Re: Lens Multiplication Factor Explained Once and for All

I think it was well said. I think some of the terminology could be improved by a seasoned writer, but that is nit picking.

I just wish that this was posted somewhere on this site for people to refer to. This is questioned so often, it would be nice to be able to point to it easily.

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Chris, Broussard, LA

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Re: Lens Multiplication Factor Explained Once and for All

I have been thinking of another aspect of DX vs FX. For a given image size you have to enlarge the picture more on DX. This seems to me to reduce the sharpness of the picture compared to using the full coverage of a full frame lens. This might explain people that have said that their old lenses seem sharper on the D700 than on the D300. Seems to me this is independent of the resolving power of the sensor.

Sort of like medium format has a higher resolution than 35mm even though the lenses are not necessarily sharper. Even the Hasselblad-Zeiss lenses on 35mm do not impress me, but on the larger real estate film there is no comparison.

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Re: Lens Multiplication Factor Explained Once and for All

Ludwig Beck wrote:

I have been thinking of another aspect of DX vs FX. For a given image
size you have to enlarge the picture more on DX. This seems to me to
reduce the sharpness of the picture compared to using the full
coverage of a full frame lens. This might explain people that have
said that their old lenses seem sharper on the D700 than on the D300.

Yes, this is how it works. The increase in enlargement from the DX format also leads to less DoF.

Seems to me this is independent of the resolving power of the sensor.

I don't think so. The D300 has more resolving power on its sensor which to some degree compensates for the increase in enlargement needed, but all in all the D700 wins. Also the D700 is less demanding on the lenses.

Sort of like medium format has a higher resolution than 35mm even
though the lenses are not necessarily sharper. Even the
Hasselblad-Zeiss lenses on 35mm do not impress me, but on the larger
real estate film there is no comparison.

Yes.

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Re: Lens Multiplication Factor Explained Once and for All

It will make more sense if you quit referring to it as a magnification factor and begin calling it a crop factor. The small sensor crops the image just like you would do with the enlarger in a dark room to get rid of outside data to keep the focus of the photo on the smaller center section.
--
Alan, in Montana
Photos are cached here,

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Re: Lens Multiplication Factor Explained Once and for All

I for one would have preferred using the field of view in degrees instead of fiddling around with equivalent focal length. Only those who have experience with a 35 mm camera have any meaningful understanding of equivalent focal length.

Other people with just limited experience have "learned" that a moderate wide angle lens (like 35 mm) do distort and still believe it will do that on DX, while the fact is that perspective is the cause of any "distortion". I suppose the same people don't think a 15 mm lens on a P&S will distort.
By using the diagonal angle of view we have

• for 35 mm (FX)

focal length; angle of view (degrees)

14 mm ; 114
18 mm ; 100
24 mm ; 84
35 mm ; 63
50 mm ; 47
85 mm ; 29
105 mm; 23
300 mm; 8.2

• for DX

10 mm ; 110
12 mm ; 100
14 mm ; 91
18 mm ; 77
24 mm ; 61
35 mm ; 44
50 mm ; 32
85 mm ; 19
200mm; 8.1

• for Canon 40D

10 mm ; 106
12 mm ; 96
14 mm ; 87
18 mm ; 73
24 mm ; 58
35 mm ; 42
50 mm ; 32
85 mm ; 18
200mm; 7.7

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Re: Lens Multiplication Factor Explained Once and for All

FlossTycoon wrote:

It will make more sense if you quit referring to it as a
magnification factor and begin calling it a crop factor. The small
sensor crops the image just like you would do with the enlarger in a
dark room to get rid of outside data to keep the focus of the photo
on the smaller center section.

Well, I think the higher magnification which is a consequence of the cropping is an important part of the explanation. The higher magnification is the reason for the reduced DoF on DX (with the same focal length, distance and f/stop), better sharpness from FX, less demand on the lens for FX, and so on.

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Re: Lens Multiplication Factor Explained Once and for All

So when I mount a DX lens on a DX format camera the physical characteristics do change ? Well obviously not . . .

I think "amount of image that falls on the sensor" is a weird concept that you should revise. How much image is there in the first place ?

By the time you get to version 10 or so I'm sure it will be golden

ChicagoNikonGuy wrote:

In Conclusion:

When an FX format lens is mounted on a DX format camera the physical
characteristics of the lens (focal length and magnification) does not
changed. The only thing that changes is the amount of image that
falls on the sensor.

Mounting a 120mm FX format lens on a DX format camera does not make
the lens a 180mm lens.

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Re: Lens Multiplication Factor Explained Once and for All

I agree with you completely. Multiplication factor and/or magnification are inherently misleading. Angle of view is a much better description and would be much less confusing.

FlossTycoon wrote:

It will make more sense if you quit referring to it as a
magnification factor and begin calling it a crop factor. The small
sensor crops the image just like you would do with the enlarger in a
dark room to get rid of outside data to keep the focus of the photo
on the smaller center section.
--
Alan, in Montana
Photos are cached here,

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Two assumptions need to be clarified

One assumption is that the aspect ratio is the same: true in the examples here but not across formats. People wanting to understand angle of view with lenses for large format, medium format or 35mm (the baby back in the day) knew that ratios differed. Therefore you cannot state an absolute equivalence without stating your assumptions about cropping (including not cropping) from a given aspect ratio.

Two: that a lens is used with a format smaller than the image circle it's been designed for. The notion of "cropping" only makes sense in these cases. Lenses used for the format they were designed for do not "crop".

Granted, I'm an interloper on this forum. But I like Nikons and have owned one Nikon rangefinder, three Nikon SLRs, about 10 Nikkor lenses and one Coolscan V ED.
--
W Alex Stewart

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Re: Lens Multiplication Factor Explained Once and for All

Nicely said.

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definition of focal length is wrong

ChicagoNikonGuy wrote:

The focal length of a lens is the effective distance from the front
surface of the front lens element to the focal plane of the camera.
This distance can be greater than the physical distance due to the
magnification factor of the lens elements used.

This is not the correct definition of focal length, as it is used (and marked) on camera lenses. In air, the lens focal length is the distance from the lens's rear principal plane to the (rear) focal plane (in a camera, the location of the sensor) when the lens is focused at infinity. The vertices (i.e. the surfaces of the front and rear lenses) don't have anything to do with the particular focal length we're talking about here.

You don't mention the word "crop", which I'm thankful for. But as an aside, I personally think there's also a problem with using the 35mm (24x36mm) frame size as the largest frame in your illustration. I'd show an image circle that covers 4x5 or even 8x10 inches and then show the smaller frame formats inside that.

This might help people realize that the angle of view captured by a lens is simply a function of its focal length combined with the area of the film or sensor format it is currently being used with -- it has nothing to do with the 35mm format per se and "cropping" is the wrong concept for what happens when you use a lens with different formats. You can, for example, use most Nikon FX-compatible lenses with sensors quite a bit larger than the FX sensor (because they cast image circles that are actually a fair bit larger than a 35mm frame size). If you do so, the lenses see a wider angle of view than they do on an FX sensor. What do you call that? An "uncrop"? A "decrop". An "opposite crop"? Doesn't make any sense, which is why I don't like the word "crop" in this context. It's just wider or narrower angles of view, depending on the size of the sensor you are currently choosing to use with the lens. Simple.

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Re: Lens Multiplication Factor Explained Once and for All

The image circle created by a 35mm format lens is shown.
The blue rectangle shows what a 35mm film, or a full-frame digital
SLR will record.
The inner red frame shows what a digital SLR with a 1.6X
magnification factor will record.

Now let's say each has the same number of pixels. What happens to the total (optical and digital) magnification factor of the system for equal size prints?

The focal length of a lens is the effective distance from the front
surface of the front lens element to the focal plane of the camera.

Hm...

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C larification

Eamon Hickey wrote:

ChicagoNikonGuy wrote:

The focal length of a lens is the effective distance from the front
surface of the front lens element to the focal plane of the camera.
This distance can be greater than the physical distance due to the
magnification factor of the lens elements used.

This is not the correct definition of focal length, as it is used
(and marked) on camera lenses. In air, the lens focal length is the
distance from the lens's rear principal plane

This is actually the "rear" nodal point. In fact, there are two different nodal points, depending on the use of the lens ( normally mounted or reversed. )

This, apart from barrel construction, partly explains why a reversed 50mm can only be used for macro work. Some reproduction lenses normally used to shoot prepress layouts were perfectly symmetrical, therefore could be used one way or the other.

to the (rear) focal plane (in a camera, the location of the sensor) when the lens is
focused at infinity. The vertices (i.e. the surfaces of the front and
rear lenses) don't have anything to do with the particular focal

You don't mention the word "crop", which I'm thankful for. But as an
aside, I personally think there's also a problem with using the 35mm
(24x36mm) frame size as the largest frame in your illustration. I'd
show an image circle that covers 4x5 or even 8x10 inches and then
show the smaller frame formats inside that.

This might help people realize that the angle of view captured by a
lens is simply a function of its focal length combined with the area
of the film or sensor format it is currently being used with -- it
has nothing to do with the 35mm format per se and "cropping" is the
wrong concept for what happens when you use a lens with different
formats. You can, for example, use most Nikon FX-compatible lenses
with sensors quite a bit larger than the FX sensor (because they cast
image circles that are actually a fair bit larger than a 35mm frame
size).

I guess, mostly PC lenses. Many other lenses will show visible degradation in the corners on FX that indicate that the useful circle is slightly exceeded. The most notorious case is the 70-200 VR, an "almost FX" lens.

If you do so, the lenses see a wider angle of view than they
do on an FX sensor. What do you call that? An "uncrop"? A "decrop".
An "opposite crop"? Doesn't make any sense, which is why I don't like
the word "crop" in this context. It's just wider or narrower angles
of view, depending on the size of the sensor you are currently
choosing to use with the lens. Simple.

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Jean Bernier

All photographs are only more or less credible illusions

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Re: definition of focal length is wrong

Focal Length: The distance between the rear nodal point of the lens and the focal plane when the focus is set at infinity.
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Re: Lens Multiplication Factor Explained Once and for All

Iliah Borg wrote:

The image circle created by a 35mm format lens is shown.
The blue rectangle shows what a 35mm film, or a full-frame digital
SLR will record.
The inner red frame shows what a digital SLR with a 1.6X
magnification factor will record.

Now let's say each has the same number of pixels. What happens to the
total (optical and digital) magnification factor of the system for
equal size prints?

I'll risk saying, that the DX system can't be said to have higher magnification. Only on screen or on print, is the image eventually more magnified. But there will be more pixels "on target" in the DX case, if a tight crop of the bird is desired.

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Jean Bernier

All photographs are only more or less credible illusions

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on nodal points vs. principal planes

lanef wrote:

Focal Length: The distance between the rear nodal point of the lens
and the focal plane when the focus is set at infinity.
--

In most cases, the nodal points of a lens are located in its principal planes, in which case your definition and the one I quoted are in practice the same. However, my understanding is that if the medium on each side of the lens differs (i.e. liquid in front of the lens and air inside it), the nodal points may not coincide with the principal planes, and in that case your definition might not work.

Some microscopes are designed to work with oil, glycerin, or water between the objective element and the specimen, as is some optical lithography equipment (optical lithography is the process by which computer chips are made).

These two images show, respectively, an immersion microscope and an immersion lithography setup.

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Re: Lens Multiplication Factor Explained Once and for All

Here's something to think about. > > > Pixel Density Crop Factor
Not just the > > > Crop Factor.

D300x1.5 crop using a 70 to 200mm =105 to300mm but at a Higher Pixel Density Crop than on the D700/D3 that means bigger and better blow ups on the crops. Hmmm???

Pixel Density Crop Factor May be = If using a D3X ??

This means it would be better to shoot a DX lens are a FX lens on a DX camera than the other way round.

Does that mean a better Pix's at the DX crop on a D300 than an DX crop on the D700/D3 blowen up??? Yes, with normal light. More control over more pixels for a blowup.

Best Regards GO

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Re: Lens Multiplication Factor Explained Once and for All

The image circle created by a 35mm format lens is shown.
The blue rectangle shows what a 35mm film, or a full-frame digital
SLR will record.
The inner red frame shows what a digital SLR with a 1.6X
magnification factor will record.

Now let's say each has the same number of pixels. What happens to the
total (optical and digital) magnification factor of the system for
equal size prints?

I'll risk saying, that the DX system can't be said to have higher
magnification.

System is not just a camera. It includes presentation too. Limiting things to 1 factor is sort of dangerous. On a side note, shorter lenses that in addition use only the central portion of the image circle usually resolve somewhat better.

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Re: Lens Multiplication Factor Explained Once and for All

The issue may be a bit more complex than what has been stated. The ratio of the focal length to the width, or the diagonal, of the film or sensor frame determines the characteristics of the lens. By using a smaller sensor, it is not that only the image gets "merely" cropped, other characteristics determined by the ratio also change, such as the curvature one associates with wide angle lenses or the compression of perspective in telephoto lenses. The magnification gets altered. Though numerically, as the post correctly puts it, the focal length stays as, say, 300mm, but with a multiplication factor of 1.5, the lens would behave as if it was a 450mm lens in terms of perspective and magnification. Its explained in basic terms here .

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