Our chemistry teacher encouraged us to study the history and naming of the orbitals on the web. (actually, our textbook did, but that's irrelevant to the problem) I easily could find the reason behind their naming, and what their names stood for. However, some sources stated that f as in f orbitals stands for fine, while others claimed it to be fundamental. Which of these two is correct? And why did scientists gave f orbitals that name? (as you're aware, they did it due to the f block elements' emission spectrum; my question is, what was the specification of their emission spectrum?) I'm sorry if the question looks stupid, but I can't figure it out myself.
I would have to say "f" overwhelmingly stands for "fundamental" (not "fine").
An early (1915) reference is "Some Recent Discoveries in Spectrum Series" Astrophysical Journal, vol. 41, p.323
Within each of these three systems there are, in general, four different types of series, known as "principle", "sharp" (second subordinate), "diffuse" (first subordinate), and "fundamental" (Bergmann). These names are not always very appropriate; for instance the "sharp" series is often diffuse, the "fundamental" may be composed of the faintest lines in the spectrum, but this is not vital.
The fundamental series was discovered by Arno Bergmann in 1907, and is sometimes called the Bergmann series. It was named "fundamental" by William M. Hicks, I beleive in A Critical Study of Spectral Series. Part I: The Alkalies H and He (1911): "F is the symbol for the new series (fundamental) as P.S.D. stand for those already known" (page 57) and "It was my first impression that this would be the same for all the alkalies and the .987 of the earlier discussion. It would be the basis of a fundamental series for each element, and the letter F which has been attached to it had its origin in this idea." (page 94).
The names existed before orbital theory. There is no need to investigate f-block elements to observe excitations to f-orbitals. Electrons of any elment can be excited to an f-orbital. In fact, Bergmann discovered the series in the sodium spectrum. What was orginially known as the sharp series, were transition to s-orbitals, the primary series transitions to p-orbitals, etc.
See The Origin of the s, p, d, f Orbital Labels for additional information.