The Earth rotates relative to the Sun at 15° per hour. It takes 4 minutes to move by 1°. The Sun has a diameter of 0.5° so it appears to move one diameter in 2 minutes. That limits the ability to read the position of the shadow on a sundial.What would be the maximum accuracy that can be achieved by making a sundial larger?
The wavelength of light is so short, and the spectrum so wide, that it has no effect on the accuracy of a sundial. You can improve the accuracy by replacing the plate gnomon with a cylindrical style, and replacing the flat plate with part of a graduated cylinder about the style axis. If the diameter of the style is selected to be 0.5° when viewed from the scale, the shadow of the style will not be asymmetric but will have the mid-line darkest, with light either side. That will improve the resolution by a factor of 4 or more. It would cancel edge diffraction effects, if they were visible, but it cannot reduce the horizon refraction in the few minutes after dawn or before dusk.We have the numbers for sun diameter etc which translate into an angle and the angle translates into 2 minutes of time precision. What are the numbers for the effect due to the wave nature and wavelength of light?
That angle will be 90°, but it effects only a thin skin about one micron thick, and then only if the edge is optically straight, and a perfect conductor. Illumination falling in the shadow will be less than 0.1% of that of the sunlit area, so you will not notice it.Wow! That angle is big.
You are saying it would be harder to see than I am.No it won't be 0.1%, it'll be 0.01% at 120 degrees. Without sources to back them up, such numbers are not appreciated.
There is no such thing as fully shadowed. A cloud in the sky to one side and clear of the sun, a nearby building, or an observer wearing a white shirt, will change the level of illumination of the shadow. That will change the critical threshold.Image processing software could easily find the location of the mid point between fully lit and fully shadowed to high precision but not the human eye, unless specially trained and if the sundial is the right size.
The light is diffracted as it crosses the knife edge. The light is initially at 90 degrees to the plane of the knife. It then turns to fill the shadow behind the knife. If you measure the angle relative to the plane of the knife the direction becomes 0° or 180°, not 120°. The light still only changes direction by 90° on passing the edge.The 0.01% is arbitrary of course, and so is the 120 angle measured from the plane of the knife.
“Electronic Transmission Technology; lines, waves and antennas”. By William Sinnema. 1979. Chapter 8.Where is the diffraction chart?