The present invention relates to an optical component having a crosslinked anti-fog coating obtainable by covalent attachment of a silane derivative of the formula (2) to the surface of the optical component and crosslinking of adjacent molecules: RoXmSiBn  (2) wherein m=1 to 3, n=1 or 2 and o=0 or 1, with the proviso that m+n+o=4; the radical X is selected from halogen or C1-4-alkoxy, and for m=2 or 3 the individual radicals X may be identical or different, the radical R is C1-4-alkyl, the radical B has the structure -B1-B2, in which -B2 is a terminal hydrophilic group which is crosslinked to at least one hydrophilic group of an adjacent molecule of the anti-fog coat, and -B1- represents either a spacer group, which joins the hydrophilic group B2 to the Si atom, or a covalent bond, where the terminal hydrophilic group -B2 is poly(meth)acrylate, and for n=2 the individual radicals B may be identical or different.