To solve the problem, we need to apply Snell's Law, which relates the angles of incidence and refraction to the velocities of light in different media. Snell's Law is given by the formula: \[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \] Where: - \( n_1 \) is the refractive index of the first medium (air in this case), - \( n_2 \) is the refractive index of the second medium (glass), - \( \theta_1 \) is the angle of incidence, - \( \theta_2 \) is the angle of refraction. ### Step 1: Calculate the Refractive Indices The refractive index \( n \) of a medium can be calculated using the formula: \[ n = \frac{c}{v} \] Where: - \( c \) is the speed of light in a vacuum (approximately \( 3.0 \times 10^8 \, \text{ms}^{-1} \)), - \( v \) is the speed of light in the medium. **For air:** \[ n_1 = \frac{c}{v_{\text{air}}} = \frac{3.0 \times 10^8 \, \text{ms}^{-1}}{3.0 \times 10^8 \, \text{ms}^{-1}} = 1 \] **For glass:** \[ n_2 = \frac{c}{v_{\text{glass}}} = \frac{3.0 \times 10^8 \, \text{ms}^{-1}}{2.0 \times 10^8 \, \text{ms}^{-1}} = 1.5 \] ### Step 2: Apply Snell's Law Now we can apply Snell's Law: \[ 1 \cdot \sin(\theta_1) = 1.5 \cdot \sin(30^\circ) \] We know that \( \sin(30^\circ) = 0.5 \). Substituting this value into the equation gives: \[ \sin(\theta_1) = 1.5 \cdot 0.5 \] Calculating the right side: \[ \sin(\theta_1) = 0.75 \] ### Conclusion Thus, the sine of the angle of incidence \( \theta_1 \) is \( 0.75 \). Therefore, the correct option is: **D. 0.75** ### Explanation of Other Options - **A. 0.33**: This value does not correspond to any reasonable calculation based on the given parameters. It is too low for the sine of an angle of incidence when the angle of refraction is 30°. - **B. 0.50**: This value corresponds to the sine of 30°, which is the angle of refraction, not the angle of incidence. It is incorrect in this context. - **C. 0.67**: This value does not match any standard sine values for common angles and is not derived from the calculations we performed. It is also incorrect. ### Revision Summary - Snell's Law relates the angles of incidence and refraction to the refractive indices of two media. - The refractive index is calculated as the ratio of the speed of light in a vacuum to the speed of light in the medium. - For air, the refractive index is 1, and for glass, it is 1.5. - The sine of the angle of incidence can be calculated using the known sine of the angle of refraction and the refractive indices, leading to the correct answer of 0.75.