(editing or comments welcomed)
For an APS-C sensor, the equivalent of a full-frame lens of focal length F and maximum aperture N has a focal length F/1.5 and a maximal aperture N/1.5 (ie the equivalent of a FF 50mm f2.8 would be an APS-C 33mm f1.8).
A comparison, taking into account this equivalence, of existing objectives shows that the results are not as clear as one might think. However, this type of comparison is difficult.
The area to be covered by the image projected in the plane of the sensitive surface is smaller in the case of an APSC-C sensor than in the case of a 24mm x 36mm sensor. As a result, APS-C lenses designed to cover smaller sensor than full-frame ones can therefore have a smaller size. But when a same lens is used on a 24mm x 36mm sensor and a APS-C one, the resulting image are different.
Thus, the first step is to determine what is to be compared.
The second step will be how to compare.
The last step will be to make some comparisons.
I. What to compare
Angle of view
The angle of view is the angle between the lateral limits of the field embraced by the view on the sensor. When the size of the sensor decreases the angle decreases. It doesn't matter if part of the image projected by the lens is unused and located outside the sensor.
Therefore, for an APS-C lens to cover the same angle of view as a 24mmx36mm lens its focal length must be different. It is easy to show that the equivalent focal length is F/1.5, 1.5 being the ratio between the diagonal lengths of the two types of sensors.
In the following we will assume that this focal length equivalence is taken into account
The aperture of a lens is related to the illumination of the surface on which the image is projected: the photographic film or the sensor.
The aperture, the "aperture diameter" and the focal length are characteristics of the lens regardless of the size of the sensor of the camera.
Instead of "aperture diameter", we should speak of entrance pupil which is the image of the aperture diaphragm through the upstream part of the optical system.
These three values are linked by the definition of the aperture number given by the formula
aperture number =
diameter of the entrance pupil /
Confusion circle / depth of field
A photograph is not seen by (or on) the sensor[*] but usually on a print or a screen. Moreover the human eye has limits in acuity.
From the minimum angle that allows the eye to distinguish two points close together on the print, it is possible to determine the size below which a circular spot on the sensitive surface will be perceived as a point (the diameter of this spot is the circle of confusion). It must be the smaller the magnification factor of the sensitive surface to the print is large.
To have the same print size between an APS-C sensor and a full frame sensor, the magnification factor must be multiplied by 1.5. As a result the circle of confusion for an APS-C sensor is 1.5 smaller than for a full-frame sensor.
Depth of field
The depth of field corresponds to the range of distance in which a point of the scene will give on the sensitive surface a spot with a diameter smaller than the circle of confusion.
From the above, it can be shown for an equivalent focal length (F/1.5), the equivalent aperture to obtain the same depth of field with an APS-C lens is equal to N/1.5, N being the aperture of the equivalent full frame lens.
In the following we will assume that this aperture equivalence is taken into account
Photographic lenses come with different characteristics, the most obvious are the presence or not of a stabilization mechanism, or of an autofocus mechanism. These two mechanisms usually involve dedicated optical elements.
Moreover, the lenses can have other optical elements to correct the inevitable optical aberrations.
Finally, the types of lenses used can be different, even talking about rarer solutions such as elements taking the form of Fresnel lenses.
II. How to compare
(to be eventually completed)
It would undoubtedly be desirable to compare the lenses according to their optical element. However such a comparison, in addition to the important work that it supposes, finds its limit indeed the optical formulas are never completely identical. This is why the comparison retained at this stage is very rough and based only on the weight of the lenses. A good part of this weight is that of the optical elements
(to be eventually completed)
In the following, the equivalences introduced above are taken into account for each pair of objectives.
Canon EF 70-200mm F4L IS II USM: Weight 780 g
Fujifilm XF 50-140mm F2.8 R LM OIS WR: Weight 995 g
Canon EF 85mm F1.8 USM: Weight 425 g
Fujifilm XF 56mm F1.2 R: Weight 405 g
Voigtländer 50 mm / 1:2,0 APO-Lanthar aspherical VM: Weight 288 g
Voigtländer Nokton 35mm F1.2 X mount: Weight 196g
Taking into account the equivalences, data of existing lenses shows that the results are not as clear as one might think.
[*]: There is a different approach to the one mentioned above for the sharpness. In this approach what is sought is not the perception of the image by the observer taking into account the magnification and the visual acuity but more simply the production of an image file as sharp as possible. In this case the limiting factor is no longer the visual acuity of the observer but the size of the sensor pixels. Some cameras of the Fujifilm X range allow to define the range of sharpness either from the photographic approach or from this last approach.