While it is true that both sentences contain compound subjects, the
singular verb is perfectly correct in both cases. The singular verb
can be used because “dust and dirt?and “light and water?can be considered
one unit, thereby calling for a singular verb. Quirk et al. (A Comprehensive
Grammar of the English Language. Longman, 1985) discusses this
principle of notional concord in Sections 10.35?0.39.
If, however, the speaker considers the nouns of the subject to be separate
entities, a plural verb could also be used, as in these examples from
“Your fairness and impartiality have/has been much
“Law and order has/ has been established.?
So either the singular form of the verb or the plural form can be used;
it depends on whether the speaker thinks of the subject as one unit
or as more than one unit.