Polymerizable Compositions, Cured Products Obtained Therewith, And Use Of These Materials

[Problem] To provide a polymerizable composition having an excellent transparency in near-infrared wavelength and excellent heat resistance, and a method for producing the same. [Means of Solving the Problem] A polymerizable composition includes: a reactive silicone compound obtained by polycondensing a diaryl silicic acid compound of Formula [1] below with a silane compound, selected under compounds of Formula [2] and Formula [2b] below in the presence of an acid or a base; and (b) a compound having at least one polymerizable group selected from the group consisting of alkenyl group and (meth)acryl group, wherein Ar1 and Ar2 are independently a phenyl group optionally substituted with a C1-C6 alkyl group, and X is a group which can undergo a hydrolytic condensation reaction, and wherein Ar3 is naphthyl or anthracyl substituted with at least one group having a polymerizable double bond, or wherein Ar3 is phenyl substituted with at least one group having a polymerizable double bond other than vinyl, or is phenyl substituted with at least two groups having a polymerizable double bond.