Problem 5.32 — Brewster’s Angle

Problem Statement

Find Brewster’s angle for a glass surface ($n = 1.6$) in air. At this angle, reflected light is completely polarized.

Given Information

• See problem statement for all given quantities.

Physical Concepts & Formulas

This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to units and sign conventions.

• See the step-by-step solution for the specific equations applied.
• All quantities are in SI units unless otherwise stated.

Step-by-Step Solution

Step 1 — Identify given quantities and set up the problem: Brewster’s law: $\tan\theta_B = n$.

Step 2 — Apply the relevant physical law or equation: $$\theta_B = \arctan(1.6) \approx \boxed{58°}$$

Step 3 — Solve algebraically for the unknown: At this angle the reflected beam is 100% polarized with $\mathbf{E}$ perpendicular to the plane of incidence.

Worked Calculation

$$\theta_B = \arctan(1.6) \approx \boxed{58°}$$

$$\text{Numerical result} = \text{given expression substituted with values}$$

$$\boxed{\theta_B = \arctan(1.6) \approx \boxed{58°}}$$

Brewster’s law: $\tan\theta_B = n$.

$$\theta_B = \arctan(1.6) \approx \boxed{58°}$$

At this angle the reflected beam is 100% polarized with $\mathbf{E}$ perpendicular to the plane of incidence.

Answer

$$\theta_B = \arctan(1.6) \approx \boxed{58°}$$

Physical Interpretation

The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.