cropped sensor - Does the imaging circle size change when a lens zooms?

When a zoom lens is designed for a cropped (APS-C) imaging circle, does the imaging circle necessarily stay that small throughout the zoom range?

It is easily understandable that a prime lens designed for an APS-C camera, like the Nikkor DX 35mm F/1.8G, would have a smaller imaging circle than a full-frame lens such as the Nikkor 35mm F/1.4G.

However, how does this work for zoom lenses? Take the Nikkor DX 16-85mm for example. It is a DX lens designed for APS-C camera but when you zoom past 24mm (16 times the 1.5X crop), wouldn't the imaging circle get big enough for a full-frame sensor? Or not? Why?

Finally, what would be the angle-of-view of the DX zoom at 24mm on a full-frame camera, if the imaging circle was sufficient to cover the whole sensor area. Currently, many Nikon FX crop the sensor area when a DX lens is mounted, but I am beginning to wonder if they need to do this unconditionally. Maybe they could stop cropping when the lens is zoomed past a certain point?

Answer

On some lenses the image circle does indeed get bigger as you zoom.

I know from experience the Canon EF-S 10-22 f/3.5-4.5 does this. At 12mm the image circle is big enough for a 1.3x crop APS-H sized sensor and by 15mm it is big enough for a full frame 35mm sensor.

However lenses such as the EF-S 17-55 f/2.8 vignette at all focal lengths on full frame. I believe the constant max aperture has something to do with it, as otherwise the total amount of light coming out of the lens would somehow change despite the iris and entrance pupil remaining the same size.

Note that the reverse is not necessarily true, the image circle doesn't necessarily get larger with a variable max aperture lens. Some Nikon lenses contain a rear baffle to reduce flare, and this causes the same vignetting regardless of focal length. Integral petal hoods on ultra-wides can have the same effect.

Finally, assuming the DX 16-85mm does not vignette on full frame at 24mm, it will have the same angle of view as any other 24mm lens - 73.7 degrees horizontally and 53.1 degree vertically.

Conditional cropping based on focal length would produce a very strange relationship between focal length and angle of view with the lens getting wider then narrower as you zoom in!