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?
 A: 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.
A: 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.
