A cationic surfactant, cetyltrimethylammonium bromide, CTAB, forms long and stable threadlike or wormlike micelles in aqueous solution with sodium salicylate, NaSal. This system makes an entanglement network similar to concentrated polymer systems and shows profound viscoelastic behavior highly dependent on concentration of CTAB, C-D, and NaSal, C-s, and the system also is strongly flow birefringent. The shear stress, sigma(xy) and the normal stress difference, sigma(xx) - sigma(yy), were determined as functions of shear rates, gamma. Flow birefringence measurements were carried out over almost the same shear rate range with an apparatus capable of simultaneously measuring birefringence, Delta n, and orientational angle, chi. The data obtained indicate that the refractive index tenser and the stress tenser are linearly related, Delta n sin(2 chi)/2 = Co, and Delta n cos(2 chi) = C(sigma(xx) - sigma(yy)), by a stress-optical coefficient C that is approximately -3.1 x 10(-8) cm(2) dyn(-1) and is essentially independent of CD and Cs. This linearity suggests that the origin of elasticity of the wormlike micellar system is the orientation of micellar portions between entanglement points as well as a Gaussian chain network. The sign and magnitude of C are consistent with the proposed structure in which most CTA(+) ions are arranged in a radial pattern with their molecular axis mostly perpendicular to the axis of the wormlike micelle. We also estimated the persistence length of the wormlike micelle as q = 26 nn through now birefringence data.