Two transparent media A and B are separated by a plane boundary. The speed of light in those media are \( 1.5 \times 10^8\text{ m/s} \) and \( 2.0 \times 10^8\text{ m/s} \), respectively. The critical angle for a ray of light for these two media is:

The critical angle \( \theta_c \) for total internal reflection when light travels from a denser medium to a rarer medium is given by \( \sin \theta_c = \frac{n_2}{n_1} = \frac{v_1}{v_2} \), where \( v_1 \) is the speed of light in medium A (denser medium) and \( v_2 \) is the speed of light in medium B (rarer medium). Substituting the given values: \( \sin \theta_c = \frac{1.5 \times 10^8}{2.0 \times 10^8} = \frac{1.5}{2.0} = 0.750 \). Therefore, \( \theta_c = \sin^{-1}(0.750) \).