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There are some highly mathematical treatments of this question and it is usually handled as diffraction theory, but it is an interesting question to answer conceptually: The cutoff is not sharp, but generally small wavelengths need to be used to see small objects because small details have a lot of information, and long wavelengths carry very little information per unit of time. Here's an example to show why. Imagine you are blind (or just close your eyes) and try to determine what an object is by touching it with a large beachball. Let's imagine that the object is a wristwatch. No matter how many times you touch the wristwatch with the beachball, you probably won't be able to figure out what it is. If you used a smaller ball it would be much easier. If you used a ping pong ball you could pretty well determine what the object was. The same is true for microscopy; to see REALLY small stuff you need electrons to do the looking.

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Q: Why does wave length determine minimum size an object can be seen?
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