What happens when $CO_2$ is passed through lime water in limited amount?

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(N/A) When $CO_2$ is passed through lime water in limited amount,the lime water turns milky due to the formation of insoluble white precipitates of calcium carbonate.
The chemical reaction is as follows:
$Ca(OH)_2(aq) + CO_2(g) \to CaCO_3(s) \downarrow + H_2O(l)$

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