Would it nearly instantly become unfocused, or would it be more or less gradual?


Past infinity sounds magical, but it's really not. Here's a thought experiment: what does something five feet away look like when you focus somewhere past that? Focusing past infinity simply means that you've focused further away than everything; nothing is in sharpest focus.

Would it nearly instantly become unfocused, or would it be more or less gradual?

As you turn the focus past infinity, things that were in focus gradually become defocused. This is exactly the same as if you are focused on that thing five feet away and then turn the focus to six, seven, eight... feet.

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Whelp... Hiroshi Sugimoto did a series focused at what he refers to as "Twice Infinity". In his notes here he states-

I set out to trace the beginnings of our age via architecture. Pushing out my old large-format camera’s focal length to twice-infinity―with no stops on the bellows rail, the view through the lens was an utter blur―I discovered that superlative architecture survives the onslaught of blurred photography. Thus I began erosion-testing architecture for durability, completely melting away many of the buildings in the process.

So, at least for large format images, his series illustrates what 'focusing past infinity' looks like.

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The exact nature of the image would depend on the lens and what you're pointing at.

Depth of Field effects will still come into play for the first bit past a lens's infinity point: Stuff close to the lens will have already been out of focus, but the edge of the horizon may still look okay initially.

Eventually you'll pass a point where any point light source in the scene will hit your focal plane as a circle larger than what could be considered 'a point', and continue to grow the more you push it.

For a more complete understanding, I suggest considering getting an older simple lens and building a 'camera obscura' out of cardboard. This can be used to look at a point like, such as a radio tower, on the horizon.

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    Note: Many manual lenses have a hard infinity stop which should prevent focussing past infinity. – flolilo Mar 8 '19 at 0:23

The job of the lens is to project an image of the outside world onto the surface of film or digital image sensor. It does this by handling every point of the subject (vista) individually (a point is so small it has no dimensions). As the light from each point on the vista traverses the lens, its path is altered. We can draw a trace of these rays. They leave the point on the subject diverging ( < ) they traverse the lens and the shape of the lens, and the density of the glass causes the rays to converge ( > ).

Inside the camera the rays converge and spread out again ( >< ). We focus by moving the lens towards or away from the flat surface of the light sensitive medium. We will get a tack sharp focused image if the apex of the cone of image-forming rays just kisses the surface of film or digital sensor. If we are not focused, the converging and then diverging cone of light rays is intercepted before or after the apex. In other words, each point on the subject should reproduce as a point on the image plane. If the rays fall short or long, we do not get an image point -- instead, we get a circle.

Thus the lens projects an image that consists of countless tiny, or not so tiny, circles. Each has scalloped boundaries due to uncorrected lens aberrations. Each is juxtaposed to its neighbors. What we see is a hodgepodge of tiny and not so tiny image points. Each is called a circle of confusion. If they are big, they will be visible as circles and not points. If we are able to make them out as circles and not points, we declare the image to be un-sharp. If they are seen as points and not circles, we pronounce the image tack sharp.

It makes little difference if the image forming rays are intercepted too soon or too late. The resulting un-sharp image will be declared fuzzy. If the lens has no infinity stop, and you were able to rack the lens so that it is positioned too close to the medium, you get a fuzzy image. Objects will be reproduced fuzzy and also smaller as compared to an out of focus image resulting from the lens being positioned too far from the medium.

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