Step 1: Conceptual Foundation: When unpolarized light reflects off a dielectric surface at the polarizing angle (Brewster's angle, \(\theta_p\)), the reflected light becomes completely plane-polarized. Brewster's Law establishes a relationship between this angle and the material's refractive index. The problem requires determining the sun's angle with the horizon, which is complementary to the angle of incidence.
Step 2: Essential Formulae/Methodology: 1. Brewster's Law: \( n = \tan(\theta_p) \), where \(n\) denotes the refractive index and \(\theta_p\) is the polarizing angle of incidence. 2. The angle of incidence (\(\theta_p\)) is measured relative to the normal (perpendicular) to the surface. The angle of the sun with the horizon (\(\alpha\)) is measured relative to the horizontal surface itself. These two angles are complementary: \( \theta_p + \alpha = 90^\circ \).
Step 3: Detailed Calculation: 1. Brewster's Angle Calculation (\(\theta_p\)): Given the refractive index \( n = 1.732 \). It is noted that \( 1.732 \approx \sqrt{3} \). Applying Brewster's Law: \[ \tan(\theta_p) = n = \sqrt{3} \] The angle whose tangent is \(\sqrt{3}\) is \(60^\circ\). \[ \theta_p = 60^\circ \] 2. Angle with Horizon Calculation (\(\alpha\)): The angle of incidence (\(\theta_p\)) is the angle between the incident sunlight and the normal to the horizon. The angle between the sun and the horizon (\(\alpha\)) is the angle between the sunlight and the horizontal surface. Geometrically, \( \alpha = 90^\circ - \theta_p \). \[ \alpha = 90^\circ - 60^\circ = 30^\circ \] Step 4: Concluding Result: The angle between the sun and the horizon is 30°.