If V1 = 2, V2 = 3, and θ1 = 13.2 degrees, using Snell's law, θ2 is approximately?

If V1 = 2, V2 = 3, and θ1 = 13.2 degrees, using Snell's law, θ2 is approximately?

• A. 20 degrees
• B. 30 degrees
• C. 40 degrees
• D. 60 degrees

Answer: (A)

Snell's law connects how a wave changes direction at a boundary with the speeds in the two media. It can be written as sin θ2 = (v2 / v1) sin θ1. With v1 = 2, v2 = 3, and θ1 = 13.2°, first find sin θ1 ≈ sin 13.2° ≈ 0.228. Multiply by v2/v1 = 3/2 to get sin θ2 ≈ 0.342. The angle whose sine is about 0.342 is roughly 20 degrees. So θ2 is approximately 20 degrees. Since the wave speeds up in the second medium (v2 > v1), the refracted angle increases relative to the incident angle, which aligns with the result.

Snell's law connects how a wave changes direction at a boundary with the speeds in the two media. It can be written as sin θ2 = (v2 / v1) sin θ1. With v1 = 2, v2 = 3, and θ1 = 13.2°, first find sin θ1 ≈ sin 13.2° ≈ 0.228. Multiply by v2/v1 = 3/2 to get sin θ2 ≈ 0.342. The angle whose sine is about 0.342 is roughly 20 degrees. So θ2 is approximately 20 degrees. Since the wave speeds up in the second medium (v2 > v1), the refracted angle increases relative to the incident angle, which aligns with the result.