Back Focus Distance vs Sensor Size (i.e. discussing the true iPhone crop factor)

[chip88]

It is widely known that a smaller sensor means a larger crop factor when assuming the same back focusing distance. But for products like the iPhone where the camera module is designed from scratch, why does the same hold true? Why can't the designers use a 50mm lens, and get the same FOV as a full frame by positioning the sensor closer?

I believe the answer is, "they could, but would not be able to achieve infinity focus" although I am still unsure as to the physics of why.

here's an illustration

 

[Derrel]

I think the answer is that the iPhone's designers were trying to avoid THIS form factor...with its 50mm f/3.5 lens...

 

[chip88]

I appreciate the humor but the real question is why does a smaller sensor HAVE to imply a crop factor, disregarding everything else.

 

[Helen B]

It's difficult to know where to begin. The simple answer is that you have already answered your own question - the distance between the rear nodal point and the in-focus image is determined by the distance from the front nodal point to the object and the focal length of the lens. That relationship is fixed. If you shorten the image distance (the distance between the rear nodal point and the image) while keeping the object distance the same you either have to accept an out-of-focus image or change the focal length of the lens.

Because you are shortening the back focus, you aren't just losing infinity focus, you are losing all focus.

There is truth in Derrel's humour. The longer the focal length, the larger the lens has to be at the same f-number. A 6 mm f/2 lens needs an entrance pupil of only 3 mm diameter. A 50 mm f/2 lens needs an entrance pupil of 25 mm diameter.

 

[RacePhoto]

Isn't that a modded shutter button, for a cable release on the Argus? Always wondered why digital cameras didn't have a cable release thread in the shutter button. No really, I did at first. Still wonder on the P&S that don't have an option for some electronic button. But since pretty much all of them have a 2 second or 10 second delay I guess it works.

For the OP, always believe whatever Helen B writes. (I've learned!) Then consider this, you may have the correct field of view, but you create a number of problems, including the big one, that you pointed out yourself. Loss of Infinity focus. That means you would also lose much of your long distance focus. Maybe gain some macro capabilities?

Lets say your lens right now is almost hitting the mirror. Moving the sensor closer, you now would need a mirror-less camera.

There are some serious physical limitations involved. It wasn't just a lazy camera company, making a cropped view on a smaller sensor.