Calculus Practice Test 2026 | Exam Prep Questions And Answers

Brewster's angle for an interface from air (n1 = 1.00) into glass (n2 ≈ 1.50) is about

34.0° 56.3° 45.0° 30.0°

Correct Answer:

56.3°

Explanation:

Brewster’s angle is the incidence angle at which the reflected light becomes perfectly polarized parallel to the interface. At this angle, the reflected and refracted rays are perpendicular to each other, which gives a simple relationship from Snell’s law. From Snell’s law, n1 sin θi = n2 sin θt, and at Brewster’s angle θi + θt = 90°, so sin θt = cos θi. This leads to n1 sin θi = n2 cos θi, and rearranging gives tan θi = n2 / n1. Plugging in n1 = 1.00 (air) and n2 ≈ 1.50 (glass), tan θB = 1.50, so θB = arctan(1.50) ≈ 56.3°. Therefore the Brewster angle for this air-to-glass interface is about 56.3°. The other angles don’t satisfy tan θ = 1.50 (for example, tan 34° ≈ 0.674, tan 45° = 1, tan 30° ≈ 0.577), so they aren’t Brewster angles here.

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