Note that I stated, “To those who understand equivalence…,” it seems you need to work on that. Try the links in
this earlier post.
Also note that I did not state that the aperture or focal length change with sensor size, neither of them do. But if you want to compare sizes, you need to understand that focal length is not the only factor for which you need to compensate. That's what equivalence is all about.
The focal length of a lens is the distance between the rear nodal point and the sensor, when the lens is focused to infinity. If you find a lens where that value varies with the size of the sensor behind it please let us know, until then my belief in the laws of physics will remain strong. No, the focal length does not 'shrink'. The f/number is that value divided by the maximum diameter of the aperture. Like focal length, it is an intrinsic property of the lens and does not change based on the size of the sensor behind that lens.
Maybe 'u' can get smartphone cameras with an f/1.4 lens because those cameras are magical items that shrink the focal length and defy the laws of physics. Out here in the real world, the rest of us can get smartphone cameras with fast lenses because the focal lengths of those lenses are very short. For example, the main camera in the iPhone 16 has a focal length of 6.9mm, meaning its f/1.78 lens requires a maximum physical aperture diameter of 3.9 mm. The reason the focal length can be short and the aperture can be small is because the sensor is small.
Unlike focal length and aperture that are intrinsic to the lens, field of view, depth of field, and image noise are affected by the size of the sensor. When you say 'the focal length shrinks' with a smaller sensor, what you really mean is that the field of view for a given focal length is directly proportional to the size of the sensor, i.e. a smaller sensor has a narrower FoV for the same focal length. That's why the 6.9mm lens of the iPhone 16 (~3.5x crop sensor), a 15mm lens on a Canon APS-C camera (1.6x crop sensor) and a 24mm lens on a FF camera all give the same field of view. That's equivalence in terms of field of view, or if you prefer equivalence in terms of focal length.
The thing you apparently don't understand is the just like FoV changes with sensor size, depth of field and image noise also change with sensor size. There is no free lunch. A smaller sensor doesn't magically decrease the FoV (increasing the equivalent focal length) but not affect other parameters. Equivalence.
- If you match the FoV at a given focal length you will be further away from the subject with the smaller sensor, so the DoF will be deeper.
- If you maintain subject distance at a given focal length, DoF will actually be (slightly) shallower with the smaller sensor (because of the smaller circle of confusion...but if equivalence already confuses you, best to leave CoC for another time).
- For a given scene and f/number, the smaller sensor will give the same exposure setting because that is determined by light per unit area hitting the sensor, but the noise in the resulting image will be inversely proportional to the sensor size for a given ISO. Smaller sensors are noisier.
That last point is what confuses a lot of people. What we generically call ISO is in reference to the International Organization of Standards (ISO) 12232:2019 standard (updated twice since its first release in 1998). That standard is
why different sensor sizes give the same exposure for a given scene and f/number, they are calibrated based on that standard to do so. Recall the bucket in the rain analogy – for a given scene and aperture, a smaller sensor will collect less light. If you want that scene to appear to be the same brightness in your output image, regardless of the sensor size (that is the point of the ISO standard), that means the lower amount of light captured by the smaller sensor must be amplified relatively more. More amplification means more noise.