The operable wavelength band of a wide-band half-mirror is windened by inserting, between (1) a substrate having index of refraction n.sub.sub and (2) layers with indices of refraction (n.sub.H .multidot.n.sub.L).sup.2 of the known four-film type dielectric half mirror having a construction represented by n.sub.sub /(n.sub.H .multidot.n.sub.L).sup.2 /air; alternating layers of: (a) high refractive index dielectric substances n.sub.H1, n.sub.H2 . . . ; and (b) low refractive index dielectric substances n.sub.L1, n.sub.L2 . . . ; each film having a thickness of .lambda..sub.o /2. The alternating layers to be inserted have indices of refraction related as follows:n.sub.sub .ltoreq.n.sub.H1 .ltoreq.n.sub.H2 .ltoreq.. . . .ltoreq.n.sub.HN andn.sub.sub .gtoreq.n.sub.L1 .gtoreq.L.sub.L2 .gtoreq.. . . .gtoreq.n.sub.LNThe alternating layer structures according to one of the following formulas (1) or (2) are inserted between the substrate n.sub.sub and layers (n.sub.H .multidot.n.sub.L).sup.2.(2n.sub.H1 .multidot.2n.sub.L1 .multidot.2n.sub.H2 .multidot.2n.sub.L2 .multidot.. . . 2n.sub.H(N-1) .multidot.2n.sub.L(N-1)) Formula (1)(2n.sub.L1 .multidot.2n.sub.H1 .multidot.2n.sub.L2 .multidot.2n.sub.H2 .multidot.. . . 2n.sub.H(N-2) .multidot.2n.sub.L(N-1)) Formula (2)The alternating layer structure defined by Formula (1) has a layer 2n.sub.H1 closest to the substrate, while the alternating layer structure defined by Formula (2) has a layer 2n.sub.L1 closest to the substrate.