The optical behavior of twisted nematic liquid crystals (TNLCs) is revealed through an angular scanning technique. Experimental results show that the optical rotation and degree of polarization of transmitted light are dependent on the polarization direction of incident light. The optical rotation is reciprocal, i.e., the polarization direction of incident and transmitted light can reciprocate when optical rotation is π/2. In some cases, the optical rotation is zero. The orientation of alignment layers in the TN cell can be determined from the behavior of optical rotation, which agrees with the measurement by an atomic force microscope. The experimental results are explained with the model of circularly polarized light based on the circular birefringence effect. Linearly polarized incident light is the superposition of right- and left-handed circularly polarized light. The propagation velocity of circularly polarized light in the LC is relevant to the polarization direction of incident light, so that the refractive indices of left- and right-handed circularly polarized light, n- and n+, or circular birefringence Δn(=n--n+) are not constants. As a result, when a linearly polarized light with the wavelength λ propagates through a TN cell with the cell gap l, the polarization direction of transmitted light is rotated to an angle Δθ. The optical rotation Δθ(=π(n--n+)l/λ) is dependent on the polarization direction of incident light, whereas the averaged refractive index ⟨n⟩(=(n-+n+)/2) can be independent of that. The incident light is partially linearly polarized light in our experiments, so that the degree of polarization of transmitted light varies with the polarization direction of incident light because the optical rotatory rates for the primary and secondary light beams are different.