It's hard to put reasons and interpretations behind all this, because in the end we just use formulas and numbers and check them in experiments. It's usually simpler that way.
Be aware that a longer wavelength means a lower energy. Frequency is proportional to energy, which is inversely proportional to wavelength.
> (I tried, but the wikipedia chapter is too complicated for me => trying to simplify here)
I can imagine. That stuff on the wiki is not even in every physics bachelor. It's definitely not for a general audience, but I thought it might help a little :)
> Therefore, if the photon does not have a mass but is still able to have an effect against the target body it impacts with, then the photon must lose energy, right?
Yes, or gain it if it slows down the object, if the object is traveling towards the light.
Or the internal energy of the object is changed. This happens when a photon is absorbed.
A photon's momentum is related to its wavelength, not it's speed. They all have the same speed in a vacuum.
2)
Sure.
> So, a remix of the original question, haha: if we say that a photon has no mass, but at the same time we say that momentum needs mass, then if we say that a photon has momentum we're screwed, no?
We would be screwed, but momentum doesn't need mass.
That's not true, it wouldn't conserve energy. The kinetic energy of the object that's hit changes, so the light must lose or gain energy. I think for a reflection this must be because of a red- or blueshift.
> What you're referring to is light absorption, which is a different effect that raises the temperature of the target object and red-shifts the incoming photon.
Absorption usually means a whole photon is absorbed, not redshifted. A lower energy photon can sometimes be emitted after absorption (however the direction and phase relation with the previous photon are lost)
Very nice. I think there are some typos though, below
"Here were some of them, along with their continued fractions."
Two of the shorthand notations for the continued fractions and the last decimal expansion are wrong. Or I'm crazy.