A ray of light, which is traveling in air, is incident on a glass plate at a 45° angle. The angle of refraction in the glass

Question

BlackTom AI · Accepted Answer

Snell's law, n1 sin θ1 = n2 sin θ2, governs refraction at an interface. 1) Relevant knowledge points and concepts - Snell’s law relates the indices of refraction (n) and angles measured from the normal: n1 sin θ1 = n2 sin θ2. - Air has n ≈ 1.00; typical glass has n ≈ 1.5 (greater than air), so light slows and bends toward the normal when entering glass. - Bending toward the normal means the refracted angle θ2 is smaller than the incident angle θ1. 2) Complete reasoning process step by step - Identify medium 1 (air) and medium 2 (glass). Use Snell’s law with θ1 = 45°. - Because n2 > n1, sin θ2 must be smaller than sin θ1, so θ2 < θ1. 3) Calculations with intermediate steps - n1 = 1.00 (air), n2 ≈ 1.50 (glass), θ1 = 45°. - Apply Snell’s law: 1.00 · sin(45°) = 1.50 · sin(θ2). - sin(θ2) = sin(45°) / 1.50 = (√2/2) / 1.5 ≈ 0.70710678 / 1.5 ≈ 0.47140452. - θ2 = arcsin(0.47140452) ≈ 28.1°. - This numerical result confirms θ2 < 45°. 4) Why the correct answer is correct - Because glass has a higher refractive index than air, the sine of the refracted angle is reduced by the ratio n1/n2, producing a refracted angle smaller than the incident angle. The calculated value (~28.1°) explicitly demonstrates this. 5) Why the other options are incorrect - “Is greater than 45°”: would require n2 < n1 (light going into a less dense medium), which is not the case for glass from air. - “Is equal to 45°”: would require n2 = n1 (no optical contrast), not true for air to glass. - “Could be any of these; depends on the index of refraction of glass”: while angles generally depend on indices, for a glass plate (n > 1) the refracted angle must be less than 45°. 6) Conclusion - The angle of refraction in the glass is less than 45°. This matches the provided correct answer: is less than 45°.

A ray of light, which is traveling in air, is incident on a glass plate at a 45° angle. The angle of refraction in the glass单项选择题

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