Karl Merz, the talented editor of Brainard's Musical World, replies to a correspondent as follows: The name of the instrument you refer to is 'laryngoscope.'

It was Garcia, the singer, who first attempted to obtain a view of the interior of the human throat and its vocal organs. His aim was to perfect vocal instruction, to solve the problem of the human voice. Garcia's methods, however, were not satisfactory. For this reason experiments were given up, and for a while neither scientists nor artists paid much attention to the laryngoscope. The idea of this instrument did not, however, originate with Garcia. As early as 1807 physicians made attempts at laryngoscopic investigation, and physicians again took up the subject after Garcia had dropped it. The two men that distinguished themselves most in this field were Dr. Turk, of Vienna, and Dr. Czermak, of Pesth. Garcia had used sunlight in his experiments, and to this practice Dr. Turk adhered. Czermak, on the other hand, used lamps and reflectors, because daylight, in his opinion, was not always suitable for experimenting. There arose a bitter debate between these two opponents, which gradually attracted the attention of scientists and singers all over Europe. By this means the laryngoscope was once more brought prominently before the world, and from that time on it was never again lost sight of. The artificial light theory carried the day. 

Many experiments have been made with this instrument. Persons have sung and talked while they had the mirror in their mouths, the vocal chords have been watched, and much valuable information has been obtained, for all that musicians have not yet reached a uniform theory as to the voice and its registers, and the professors the doctors, and voice-builders, are still at variance. It is the opinion of not a few, that the laryngoscope is of no practical value to the vocal teacher, inasmuch as the person that is operated upon, having to stretch out the tongue, and a glass being placed in the mouth, cannot produce a natural tone. You had better let the laryngoscope alone. It is of far more importance for you to know what a pretty tone is, how to sing with expression, than to know how the vocal chords move or vibrate. From what information I could gather on this subject, it seems that the laryngoscope has done far better service to medical science than to musical art.

—Karl Merz, "The Laryngoscope," Werner's Voice Magazine, January, 1881: 3. 

You may think it strange, but I read articles like the one above and ask myself: Ok, so what has changed? 

A lot, certainly. 

Technology has progressed insofar as that examination of the vocal tract and larynx is not invasive, with scoping being done via the nose and nasal passage. But does this technological advance help the singer sing? I would say no. And therein lies the rub. 

Analyzing tone is one thing, while creating it is another. They aren't the same process at all. However, it's not uncommon to encounter the belief that knowledge of the muscles of the larynx and vocal tract enable greater control. Experience in the studio tells me, however, that this is an illusion. You can tell a student how the muscles of the larynx work, but this doesn't give them the means to sing any more than a knowledge of the muscles of the leg and foot help a person to walk or run.

"You can't control the voice. You can only control what it wants!" —Margaret Harshaw

Truer words were never spoken. 

Finding out what the voice wants? You need a really good teacher for that. Either that, or you are a canny autodidact.