A beginner's guide to "is equal to" vs "is equivalent to".

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A beginner's guide to "is equal to" vs "is equivalent to".
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A recent thread has spawned some confusion on the use of the word "equals" with respect to focal length and relative aperture.  This often causes confusion for people when using FF lenses on APS-C cameras, so I thought it would be helpful to discuss this bit of terminology.

First off we have to discuss the "crop factor".  APS-C has a "crop factor" relative to FF of 1.6 for Canon and 1.5 for everyone else.  The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo.

However, the crop factor can also be described in terms of what lens and settings you would use on FF to get the same results.  The way in which you do this is to multiply the focal length and relative aperture of the lens by the crop factor.  For example, a lens at 85mm f/2.8 on Canon APS-C (crop factor = 1.6) will be *equivalent to* (as opposed to "equal to") a lens at 136mm f/4.5 on FF.

What this means is that while the lens is actually at 85mm f/2.8, the *effect* of those settings on Canon APS-C, in terms of the appearance of the resulting photo, is the same as if you had used 136mm f/4.5 on FF from the same position with the same exposure time (the equivalent ISO setting, for the same lightness in the photo, will change by the square of the crop factor, in this example, 2.5x).  The lens itself has not changed, but the *effect* of the lens settings has changed, relative to the effect on FF.

So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like:  85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF.  The actual lens settings remain 85mm f/2.8 1/400 ISO 800, but had you taken a photo of the same scene from the same position with FF at 136mm f/4.5 1/400 ISO 2000, the perspective, framing, DOF, motion blur, lightness, and noise* would all be the same.

This is true whether or not the lens was specifically designed for FF or APS-C.  For example, if you used a 50 / 1.4 lens designed for FF or a 50 / 1.4 lens designed for APS-C, nothing changes.  If you put a 50 / 1.4 designed for FF or a 50 / 1.4 designed for APS-C on an APS-C camera, the effect of both the focal length and relative aperture remain unchanged.  The equivalence is only for comparing the effect of a lens used on one format to the effect of a lens on another format.

I hope this helps with regards to any confusion between "is equal to" and "is equivalent to"!

*For equivalent settings, the same total amount of light will be projected on the sensor which will result in the same noise *if* the sensors record the same proportion of that light and add in the same amount of electronic noise (the additional noise from the sensor and supporting hardware).

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tko
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