Step 1: Recall Lucas reagent and the reaction.
Lucas reagent is anhydrous $ZnCl_2$ dissolved in concentrated $HCl$. It converts alcohols to alkyl chlorides: $ROH + HCl \xrightarrow{ZnCl_2} RCl + H_2O$. The insoluble $RCl$ makes the solution turbid.
Step 2: Different alcohols react at different rates.
Tertiary alcohols form stable carbocations instantly, giving immediate turbidity. Secondary alcohols react within a few minutes (delayed turbidity). Primary alcohols react very slowly and show no turbidity at room temperature. This difference in rate allows easy distinction.
Step 3: Eliminate other tests.
Fehling's test detects aldehydes (reduces $Cu^{2+}$ to $Cu_2O$). Tollens' test detects aldehydes (silver mirror). Hinsberg's test distinguishes amines. None of these work for alcohols. Only the Lucas test distinguishes primary, secondary, and tertiary alcohols.
\[ \boxed{\text{Lucas test}} \]