A composition for an anti-reflective coating or a light absorbing coating, which shows good light absorption for lights of 100-450 nm in wavelength, suffers neither footing nor intermixing, and has excellent storage stability and step coverage, and novel copolymers to be used therein. The novel polymers comprise acrylic or methacrylic copolymers or terpolymers, at least having both recurring units (1) wherein an amino group- or hydroxyl-group containing organic chromophore capable of absorbing lights of 100 to 450 nm in wavelength is chemically bound to the carbonyl group bound to a carbon atom in the main chain, directly or through —R1NHCXY— (wherein R1 represents an alkylene group, X represents O or S, Y represents O or NR6, R6 represents H, a substituted or non-substituted, straight chain or cyclic alkyl group or a phenylene group) and for example recurring units (2) wherein a double bond-or epoxy group-containing alkyl group is chemically bound to the carboxyl or oxygen group bound to a carbon atom in the main chain. The composition containing the copolymer is coated on a wafer to form a bottom anti-reflective coating and, after coating thereon a photoresist, deep UV exposure and development are conducted to form a resist image with high resolution.