Check out Photographic Lenses by C.B Neblette: Paraphrased: The circle of confusion size is based on the diameter of the largest circle which will appear as a point from a given viewing distance. Basis – The average observer can resolve lines viewed from 1/3000 the distance. Some examples, a 1-inch coin viewed from 3,000 inches (250 feet). A 25mm coin from 75 meters. A 3-foot wagon wheel viewed from 1.7 miles.
In terms of a displayed photograph: The above is too stringent for pictorial photography as photographs have lowered contrast and generally viewed under indoor lighting. Generally accepted is 1/1000 of the viewing distance = 1/100 of an inch viewed from 10 inches. That’s 1/4 mm viewed from 10 inches (250mm). If the displayed image is viewed from 20 inches (500mm), then the circle size is 2/100 inches = 1/2 mm.
We can apply this to an 8x10 inch print made from a 35mm camera image. To make the 8x10 requires 8X magnification. Thus, the circle size at the image plane must be no larger than 1/800 inches = 0.32mm032mm.
If the camera used is an APS-C format, the crop factor is 1.5. For this lash-up, the magnification to make the 8x10 is 8 X 1.5 = 12X. Give this layout, the circle size is 0.32032 ÷ 1.5 = 0.2mm02mm at the image plane.
Most depth-of-field tables are based on an 8X10 inch displayed image scrutinized from 10 inches = 0.25mm circle diameter.