Step 1: Brewster's Angle Definition
Brewster's law defines Brewster's angle, \( \theta_B \), as the angle of incidence \( \theta_i \) for which reflected light is fully polarized. The formula is: \[ \tan \theta_B = \frac{n_2}{n_1} \] Here, \( n_1 \) is the refractive index of the initial medium (air, approximately 1), and \( n_2 \) is the refractive index of the transparent medium. The equation simplifies to: \[ \tan \theta_B = n_2 \]
Step 2: Snell's Law Application
Snell's law establishes the relationship between the angle of incidence and the angle of refraction: \[ \frac{\sin \theta_i}{\sin \theta_r} = \frac{n_2}{n_1} \] Given \( \theta_i = 60^\circ \), \( \theta_r \) represents the angle of refraction.
Step 3: Calculating Refraction Angle for Polarization
For complete polarization of the reflected ray, the angle of incidence \( \theta_i = 60^\circ \) must equal Brewster's angle \( \theta_B \). Consequently, the angle of refraction \( \theta_r \) is calculated as: \[ \theta_r = 30^\circ \]
Final Answer: The angle of refraction in the medium is 30°.