|MadSci Network: Astronomy|
Any object that you 'see' is emitting photons that reach your eye. An opaque object seems opaque because the photons that might be emitted from below the visible surface simply never reach your eye - for instance because they never leave the object.
This is the clue to understanding how far into an object you can see.
The Sun is a glowing ball of gas from which light is emitted. All parts of the Sun emit light of some sort but that light may very well be absorbed along the journey away from the point of origin.
Light is both 'absorbed' and 'scattered' when it passes through a gas like the Sun. 'Scattering' refers to events where photons alter their directions, while 'absorbtion' refers to events where photons are stopped by a molecule, or atom or ion or something like that and is reemitted at a slightly later time after participating in processes inside the absorbing particle. The light is emitted in a direction that is not the same, necessarily, as that from which the photon came, and therefore absorption has a 'scattering' effect as well.
Now, if light that you see is not coming in a straight line from the object you are trying to observe you will say that you cannot 'see that object', at least not clearly. This is what happens with light from deep inside the Sun. The light comes out at some time and may head towards the Earth and you, but is not carrying any directional information, about the origin of the original photon, that you would be able to form an image with of where the original photon came from. Hence you will say that you cannot 'see' the point inside the Sun from which the light originally came.
The parts of an object that you can 'see' are the last places the photons interacted with the object, which, in this case, is the photosphere of the Sun.
Light with different wavelengths interacts differently with matter. If your wavelength is right in the middle of an atomic absorption line the photons will be readily absorbed and re-emitted while photons with wavelengths beside atomic absorption lines will not be absorbed. Hence light with wavelengths not equal to absorption lines will travel further than light with wavelengths right at absorption lines. You can therefore 'see' other surfaces with light at different wavelengths, on the Sun, as the article from Wikipedia points out.
If you choose to look at the Sun in a wavelength band right at an absorption line - for instance at the wavelength of the Calcium H and K lines - you will see the surface of gas on the Sun where the photons last interacted with the Calcium ions. As there is Calcium throughout the Sun and since the absorption lines in question are strong the surface will look really firm and will be closer to you than surfaces that absorb less.
So-called solar protuberances (giant ejections of plasma from the surface of the Sun along magnetic field lines) will seem very solid indeed if you look at them in the light with wavelengths matching the Calcium H and K lines, whereas the same protuberances observed in wavelengths that do not corespond to absorption lines will seem fuzzy and indistinct.
This is the effect of the wavelength of the light you are considering that your professor spoke about. Think "where did the photons of this wavelength interact with the gas for the last time?".
Try the links in the MadSci Library for more information on Astronomy.