Telescope Reviews: Resolving a thin wire

No, you have just shined the light on the conditions that makes it possible for you to see the thin line.

What is actually happening in this situation , as you mentioned above, is that some light is reflecting off the shiny surface, both from the guitar string and the spider web. This actually makes this condition quite the opposite of the Cassini division condition, a black line across a white surface, where the black line similar to a power line reflects no light.

What happens when the thin line you've selected reflects light? Two very important conditions conspire to allow you to see this thin reflective wire.

First; It becomes similar to a long line of point sources. The light from a point source can be seen even if it has imperceptible width. If you were to attempt to measure the width of the stars, you would find it an impossible task since there is not an Earth bound telescope capable of making the measurment. Possibly Betelguese and Antares being the exceptions.

Second; A lens is not capable of showing any object smaller than it's limit of resolution. What it will do is make anything smaller than the Airy disk appear as the same size as the Airy disk. Your 50mm lens has a 2.75 arcsec radius for an Airy disk. Your lens has actually fattened up the image of the line to a diameter of 5.5 arcseconds. How has it done this? Because it is not capable of producing an image in the focal plane smaller than that 5.5 arcsec in diameter. There is no disputing this. This can be measured.

Since the object has reflected some light, the lens can see it as if it were similar to a point source, however extended in a linear manner making it even easier to see. And what you are seeing in a 50mm binocular is a fattened image of a thin line, produced by the physics of the optics to the smallest possible image the lens can show, the Airy disk. The image you see in the binocular is actually 5.5 arcseconds in angular measure, because the lens is incapable of forming any image smaller than that.

Had you used an optical system with a micrometer eyepiece, you would have been able to measure the image of your line as seen thru the eyepiece. It would have measured 5.5 arcsec and you would never have known you were looking at a wire ten times thinner than the image in your focal plane.

Addressing the physiology of the eye as detector, there is a reason you can see the wire, even though you cannot resolve it. Had you placed a 0.3mm speckle at those distances, it would be hopelessly lost. You would not see it. But you have used a thin line, one that has reflected some light. The linear condition allows an infinite number of speckles to cross over the expanse within the detectors of the eye where a single element of the same with would fall on empty space. For an object to be detected it must cross more than one detector in the eye. Your line has met that condition a hundred fold and more. So you can see it, not because you have superhuman vision, but because it is a line of an infinite number of visible points.

Moreso than anything, the reflected light allows you to see the thin wire as something other than what it truely is. This can be refered to as detection, not resolving. In this sense, your example is similar to all those observers that see the Cassini division with telescopes too small to physically resolve the width of the division. There is no doubting they can detect the Cassini division, however they have not resolved it. Their optics have made it appear fatter than it truely is, due to no fault of their own.

This discussion should belong to the thread resolution in binoculars. I cannot paste it into that thread, but I can cut it and make it its own thread.

edz

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