Differenciation between wavelength and energy: Does a photons wave-length or energy determine its refraction and absorption?

Question

I know that a photons wavelength and energy are coupled and that my question therefore could be quite ridiculous.

However, as a Biologist, I simply learned that refraction is determined by a photons wavelength (and angle, difference of medium density..) and I learned that absorption is determined by the photons energy, as the molecule's free electrons, that absorbs the photon, must be excited by an equivalent amount of energy (minus vibrations and interactions with solvent).

Here, I would like to gain a deeper understanding and therefore ask for brief additional explanations of why these two statements might be true or false, or for links to open-source further reading so that I can deepen my knowledge. Please also comment on whether there is any merit in differentiating between wavelength and energy, as this might be the exact same phenomenon, described with different words.

My second question is, whether the depicted trend in the picture (smaller wavelength -> larger refraction) is also true for the non-visible ranges in both directions (radio/x-ray). I know that the prism might not be transparent in those ranges; I am asking for a more philosophical answer.

Answer 1

Wave length and frequency are related via so-called dispersion relation, which in case of photons in vacuum (or a dispersionless media) is: $$ \nu=\frac{c}{\lambda} $$ (There are cases where this is not the case, e.g., see here, but this would go well beyond what the OP intended.)

Thus, from a physicist's point of view, talking about wavelength or ferquency of a photon is the same thing, although one or the other may be more convenient for a specific application (or simply preferred for historical reasons).

To address the second question - diffraction and refraction are general wave phenomena, which can be observed for electromagnetic waves of any frequency (take a look at the table here), but also for waves of different nature - e.g., for sound waves the air, for elastic waves in materials, wave son water, and so on. The conditions for observing this phenomena however differ: the prism shown in the image is suitable for visible light or nearby ranges - such as infrared or ultraviolet. Radio waves are much longer - they can be refracted by buildings or even the Earth's curvature. On the other hand, the X-rays are much shorter - their diffraction is usually observed on crystals (and in fact is widely used for studying crystal structure - including the protein structure in biology.)

Answer 2

whether there is any merit in differentiating between wavelength and energy

These are totally different concepts, and it may be misleading to mix them up. Wavelength depends on refractive index of the material where light is propagating:

$$\lambda=\frac c{n\nu}.$$

A light wave, propagating from one medium into another will retain frequency but will change wavelength. Absorption is defined by frequency, as it's just a change in energy level of the absorbing system, while wavelength defines the effects due to spatial distribution of EM fields: interference, diffraction, refraction.

whether the depicted trend in the picture (smaller wavelength -> larger refraction) is also true for the non-visible ranges

In the regions of spectrum where there's considerable absorption, there may be anomalous dispersion, which will reverse the trend.