Final answer:
Measuring the exact dimensions of the Galaxy's visible halo is difficult due to interstellar dust dimming the light of stars and the presence of invisible matter, like dark matter, that extends far beyond the luminous parts of the Galaxy.
Step-by-step explanation:
The difficulty in pinpointing the exact dimensions of the Galaxy's visible halo arises from several factors. First, estimating the distances to faint stars using their apparent brightness is complex because the light we observe is often dimmed by interstellar dust. This dimming can lead to underestimations of the stars' actual distance and, accordingly, the size of the Galaxy. Early astronomers made this mistake, not realizing that what they perceived as a faint star due to distance could actually be a brighter star partially obscured by dust. Another complicating factor is that much of the Galaxy comprises invisible matter. This invisible matter doesn't emit or reflect light in a way we can easily detect, further challenging astronomical measurements of the Galaxy's size.
In essence, the presence of interstellar dust and dark matter means that what we can visually observe and measure in the Galaxy accounts for just a small fraction of its total mass and volume. Lastly, our position within the Galaxy makes it difficult to obtain a clear, comprehensive view of its structure, much like how it’s tough to map a city when standing on one of its streets.