$\underset{\mathrm{Lime}}{\mathrm{CaO}}\stackrel{\mathrm{Limited} \mathrm{water}}{\to }\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$

The process is known as slaking of lime and the product is slaked lime. It is an exothermic process.

$\mathrm{Ca}{\left(\mathrm{OH}\right)}_2\mathrm{aq}$ solution is known as lime water and used for test of ${\mathrm{CO}}_2$.

$$\begin{gathered} \mathrm{Ca}{\left(\mathrm{OH}\right)}_2\left(\mathrm{aq}\right)\stackrel{{\mathrm{CO}}_2}{\to }{\mathrm{CaCO}}_3 \\ {\mathrm{CaCO}}_3+{\mathrm{CO}}_2\left(\mathrm{excess}\right)+{\mathrm{H}}_2\mathrm{O}\stackrel{}{\to }\mathrm{Ca}{\left({\mathrm{HCO}}_3\right)}_2 \end{gathered}$$

Milkiness is due to the formation of calcium carbonate and disappearance of milkiness is due to the formation of calcium bicarbonate.