# Wavelength and resolution

I'm reading some texts that seam to assume knowledge of light that I'm not too familiar with. How does wavelength of light relate to the minimum distance span that can be observed (i.e. you cannot make a lens big enough to resolve individual atoms), and is this a light phenomena or an intrinsic wave phenomena?

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This is a wave phenomenon. Suppose that you have a plane water wave. Say it hits a small object. If the object is smaller than the wavelength, it won't disturb the wave much. If the wavelength is smaller, and the object is the same size or larger than the object, then the wave will scatter off the object. I'm trying to find a video of this in a ripple tank but can't seem to find one online.

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That was kind of the response i was looking for, thanks. But is there any reason it won't disturb the wave if the object is smaller? Is there any more basic terms that can be explained in? – Andreas Hagen Oct 22 '12 at 10:16

In quantum physics one can directly relate the frequency of light directly to energy: $$E=h\nu$$ where $h$ is Planck's constant and $\nu$ is frequency.

One can also relate frequency to period:$$\nu = \dfrac{1}{T}$$ which can be related to a wavelength if one knows the phase velocity of the system:$$\nu = \dfrac{v}{\lambda}$$ The velocity of light is $c$, therefore:$$\nu = \dfrac{c}{\lambda}$$ We can plug this back into our first equation and get:$$E=\dfrac{hc}{\lambda}$$.

It is the wavelength of light that controls the resolution of system in question. The wavelength must be on the same scale or less of the feature we are trying to resolve. If the wavelength is larger than the feature, then we are unable to see the feature itself. Since the energy of light is inversely proportional to its wavelength, the smaller the wavelength, the more energetic is the light. Therefore, one needs very high energy light to resolve very small features. The allusion to the size of the lens is an allusion to a condenser in a microscope. One would need to collect a lot of light (energy) and concentrate to very high frequencies in order to make the wavelength small enough to see an atom.

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My question might have been somewhat poorly phrased, what I was wondering about is why one cannot resolve features smaller than the wavelength. Could you elaborate on this please? – Andreas Hagen Oct 15 '12 at 13:03
@Andreas Hagen I am not entirely sure what you are after. However, assuming you want a more complicated explanation then simple intuition, I would refer you to Nyquist-Shannon sampling theorem which basically tells you that your sampling interval must be at least half that of the interval in question in order to get full resolution (or alternatively the sampling frequency must be double that of the frequency in question). – user11547 Oct 15 '12 at 13:16