How do I select a fixed lens for my APS-C sensor camera for a specific field of view/zoom

Question

I have a camera that's been set up for a very specific application: it's a mirrorless Sony alpha 6000, with the lens that came with the camera: The Sony 16-50mm f/3.5-5.6 OSS Retractable Zoom Lens.

I don't need to zoom, I don't need to focus, as it will be used in a situation where I always have it focused on the same object the same distance away, and I also have it zoomed to maximum of 50mm, which according to the sony website is 32 degrees FOV.

What I would like to do is make this more 'foolproof' by replacing the lens with a fixed lens instead. I thought this would be as simple as buying a 50mm lens, but the A6000 is an APS-C sensor, which means I need to figure out what '50mm' means when the E-mount lens might be a full-frame lens, or an APS-C lens.

So my question is: Without literally buying 3 lenses and taking them home to test, do I calculate exactly which fixed lens is the same as the lens I have zoomed in? If I buy a full-frame lens, does that mean I need 35mm (50mm / 1.5), or do I get a 50mm full-frame lens? or it 50mm * 1.5 -> 75mm APS-C lens?

A few degrees field of view either way isn't a big deal.

Answer 1

There is no calculation required. If you are happy with 50mm now, just buy a 50mm "fixed' lens, as 50mm is always 50mm regardless of what the sensor size is. Yes, the field of view changes with different sensor sizes, but you are not changing the sensor, so 50mm will equal 32 degrees FOV with any 50mm lens you buy.

Due to minor differences in stated focal length, there might be some variation in the actual FOV between individual 50mm lenses.

There can also be FOV variation due to focus breathing at certain focus distances.

Either of these variations could be made up simply by moving the camera closer or farther from your subject.

Answer 2

50mm is 50mm.

ANY 50mm lens, either made for APS-C cameras or FF cameras, will give you the same 50mm angle of view on the same 1.5X APS-C camera. This will be the same angle of view that one would get using a 75mm lens on a FF sensor. You only need to get a 75mm lens if you're also going to change to a FF camera and want the same angle of view that you get with your 50mm lens on your APS-C camera.

Your 16-50mm lens has actual focal lengths ranging from 16-50mm. That gives an angle of view on your APS-C camera of a 16-50mm lens on an APS-C camera, which is also the "equivalent" angle of view given by a 24-75mm on a FF camera.

When your 16-50mm APS-C lens is zoomed to 50mm on your APS-C camera, you get the angle of view of a 50mm lens on an APS-C camera. That's the same angle of view you'd get using a 75mm lens on a FF camera.

When a 50mm FF lens is used on your APS-C camera, you get the angle of view of a 50mm lens on an APS-C camera. It's the same angle of view as you get using a 50mm APS-C lens on your APS-C camera. The only time you need to worry about conversion factor is if you want to get the same angle of view using a different sensor size.

The larger image circle of the FF lens doesn't spread the same angle of view over a larger image circle, it provides a wider angle of view over a larger image circle. The center 28mm diameter portion of the FF lens' image circle shows the same thing as the entire 28mm wide image circle cast by the APS-C lens. The extra 8mm on either side of the larger image circle shows things that are outside of the smaller image circle's coverage. But the center 28mm of both lenses' image circles show the exact same thing.¹

_{¹ This is assuming both lenses are actually the same focal length, use the same projection, and share the same geometric distortion characteristics. In practice, one 50mm lens may actually be 48mm and another 50mm lens may be 52mm in focal length. Both would be marketed as 50mm lenses.}