NOVELTY - A fluorine-containing random copolymer contains 10-75 mol% fluorine-containing structural unit (I), 4-70 mol% fluorine-containing structural unit (II), 10-70 mol% hydroxyl-containing structural unit (III), and 0.001-10 mol% silicon-containing structural unit(s) (IV)-(XI). The random copolymer has weight average molecular weight of 5000-300000 by polystyrene conversion and molecular weight distribution of 1-5.    USE - Fluorine-containing random copolymer is used for double bond-containing fluorine-containing random copolymer for varnish, coating material and coating composition for coating film (all claimed) for optical material, antireflective film, sheath material of optical fiber, protective film for glass filter, solar cell, resin varnish, and semiconductor material.    ADVANTAGE - The coating composition containing the fluorine-containing random copolymer enables to form coating film having excellent low-refractive index property, transparency, antifouling property, water-oil repellency, surface slipperiness, and abrasion resistance. The fluorine-containing random copolymer has excellent solubility and storage stability.    DETAILED DESCRIPTION - A fluorine-containing random copolymer contains 10-75 mol% structural unit of formula: -(C(-R1)(-R2)-C(-R3)(-R4))- (I), 4-70 mol% fluorine-containing structural unit of formula: -(C(-F)(-F)-C(-F)(-O-R5))- (II), 10-70 mol% hydroxyl-containing structural unit of formula: -(CH2-CH(-(CH2)p-O-R6-OH))- (III), and 0.001-10 mol% silicon-containing structural unit(s) of formulae (IV)-(XI). The random copolymer has weight average molecular weight of 5000-300000 by polystyrene conversion and molecular weight distribution of 1-5.    R1-R4=H, fluoro or trifluoromethyl, at least one is fluoro;    R5=1-30C linear or branched perfluoroalkyl or fluorine-containing alkyl optionally having ether bond;    R6=1-10C linear alkylene optionally having ether bond;    p=0-6;    R7=H or methyl;    R8,R9=1-4C alkyl, phenyl, cyclohexyl, -CF3, -CH2CF3, -(CH2)2CF3, -(CH2)3CF3, -C(CH3)3, or H;    R10=H or 1-6C alkyl;    n=1-420;    r=1-6;    m=not 0;    k=1-6;and    X,Y',Z=H or fluoro.    (i) When q is 0, m is 1-420; (ii) when q is 1-210, m is 1-210; and (iii) when X is H, at least one of Y' and Z is fluoro. INDEPENDENT CLAIMS are included for the following:    (1) coating film, which contains the fluorine-containing random copolymer and having refractive index of 1.34-1.44;    (2) manufacture of fluorine-containing random copolymer, which involves copolymerizing a polymerization component by solution-polymerizing method, using a solvent chosen from ethyl acetate, butyl acetate, xylene, toluene, methyl ethyl ketone, and methyl isobutyl ketone;    (3) double bond-containing fluorine-containing random copolymer, which is produced by reacting the fluorine-containing random copolymer and unsaturated isocyanate; and    (4) coating composition, which contains 5-95 wt.% double bond-containing fluorine-containing random copolymer, and 95-5 wt.% oligomer and/or monomer chosen from double bond-containing (meth)acrylate oligomer or double bond-containing (meth)acrylate monomer.