Step 1: Understanding the Concept:
Phenol is highly reactive towards electrophilic aromatic substitution due to the strong activating $+M$ effect of the $-OH$ group. The solvent plays a critical role in controlling the extent of bromination.
Step 2: Detailed Explanation:
1. Bromine water: In aqueous medium, phenol ionizes to form the phenoxide ion, which is even more reactive. This leads to poly-substitution, giving 2,4,6-tribromophenol (white precipitate).
2. Low polarity solvents ($CS_2, CHCl_3, CCl_4$): At low temperatures ($273\text{K}$), the ionizing power of the solvent is low. Phenol stays mostly in its non-ionized form. This limits the reaction to mono-substitution.
3. The $-OH$ group is ortho-para directing. Due to steric hindrance at the ortho position, the para-isomer ($p$-bromophenol) becomes the major product when reacted with $Br_2$ in $CS_2$ at low temperature.
Step 3: Final Answer:
The reagent is $Br_2$ in $CS_2$ at $273\text{K}$.