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Wavelength and resolution explained

Things with long wavelengths are analogous to the basketball in the cave story because neither can provide too much detail about what they hit. Things with short wavelengths are like the marbles in that they can provide you with fairly detailed information about what they hit. The shorter the probe's wavelength is, the more information you can get about the target.

A good example of the wavelength vs. resolution issue is a swimming pool. If you have a swimming pool with waves which are 1 meter apart (a 1 meter wavelength) and push a stick into the water, the pool's waves just pass around the stick because the 1 meter wavelength means that the pool's waves won't be affected by such a tiny target.

All particles have wave properties. So, when using a particle as a probe, we need to use particles with short wavelengths to get detailed information about small things. As a rough rule of thumb, a particle can only probe down to distances equal to the particle's wavelength. To probe down to smaller scales, the probe's wavelength has to be made smaller.

This is all a very hand-wavy explanation of a very difficult concept. To explain it completely would involve more math than we have space to get into.