Why should an APSC lens be larger than its 1" equivalent ?

Started Oct 21, 2017 | Discussions thread
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Why should an APSC lens be larger than its 1" equivalent ?
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Much heat lately about the G1XIII lens.

Basically, the point is (let's only take the long side of the zoom) :

• a G7X beeing f/2.8 @ 33mm (eq 72mm FF), it has an aperture of 33/2.8=12mm
• a G1XII beeing f/5.6 @ 45mm (eq 72mm FF), it has an aperture of 45/5.6=8mm

Thus with a smaller lens, the 1" G7X can gather more light wide open.

From this point, people argue :

• several think that the G1XIII lens should have been faster even given its size, since other cameras show that gathering more light with compact zooms is obviously possible (the 1" crowd, LX100, G1XII ...)
• several argue that it is more complicated and that given the laws of physics, even while not gathering more light, lenses with larger image circles have to be much larger
• others somewhere between both positions

So my question is : why should an APSC lens be larger than a 1" lens with the same absolute aperture ?

So as to settle things, please let me try to put things how I understand them, and please forgive the following approximations.

For the maths, I'd recommend Hyperphysics. Note that, while I have a decent math background and I can understand stuff like on hyperphysics, I'm no an optics engineer and I fully accept that people know things I don't. I just want to improve and my question is an actual one : please let me understand why I'm wrong. By "understand" I mean "understand", not accept a moral authority argument like a bold "these are laws of physics".

Si first, we can see many schemes with approximations of what a lens is like the following :

Thin lens with the image focal length beeing the distance between the lens and F' . The object size vs image size is the magification of the lens.

For the following, we'll assume a constant obect size, and a constant maginification, thus a constant image size.

The point is, an actual lens has a not-null thickness and is more like that :

By adjusting thickness and powers of front and rear surface, it is possible to adjust the effective focal lentgh. With the the same object and image size, here the image is formed closer to the surface, thus reducing the overall distance from the front of the lens to the image plane. Drawback (because there is no free lunch) : the incident rays on the sensor form a higher angle, making it more difficult to preserve brightness homogeneity and corner sharpness.

Actually, an actual lens is not a formal lens which would be "thick". This "thick lens" thing with a thickness and surface powers (front and back) helps to model actually composed and more complex optical systems made of glass elements which at the end behave as a thick lens but may perform "magical" internal tricks helping to reduce the image distance yet preserving low incident angles. Like this...

The optical system is made of many elements helping to preserve incident angles while keeping the image close enough to reduce the overall lens size. In a lens, the glass on the sensor side is often much smaller than the front element, because a lot of work has been performed by the preceeding elements.

Why all that ? Just to state that for an optical system, when compared to a thin "abstract" lens, an effective FL increase does not necessarily have an equivalent impact on the overall size. I understand that it has to be greater, but I don't get why it should be much greater (eg as much as for a thin lens).

So let's include a 1" sensor behind a smart optical system keeping high low incident angles yet able to project on a close sensor.

Here, the lens focuses on the 1" sensor.

What's needed with an APSC larger sensor ?

The APSC lens beeing larger, if one keeps the same incident angles, the APSC sensor has to be further and the lens needs to focus on a more distant plane. Here, the light intensity on the sensor is lower thus needing higher ISO for the same total light (the equivalence stuff).

So yes I agree, the overall distance between the front of the lens and the sensor has to increase when the sensor size rises. But how much ? As far as I understand, The higher the incident angles, the less the absolute overall size requirement (symply Thales).

And it appears that with a 17 or 18mm flanger distance (distance between the mount and the sensor) for the APSC MILC systems, the incidence angle IS not very high (sensor diagonal beeing 44mm and inner glass element size beeing not null). And we speak here about ILC systems, not compact optimized fixed lens cameras with - I guess - even smaller flanger distances yet greater incident angles.

So, the G7X incident angles having to be high, I would be very surprised if more than a few milimeters were needed so as to keep the same light gathering ability on an APSC lens. I'm sorry but I don't get why the G1XIII lens has to be so slow (except low development efforts).

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