Waves
5 marks · NormalA ray of light enters a rectangular block of glass from the air at an angle of incidence of 45°. The refractive index of the glass is 1.5.
Calculate the angle of refraction (to 2 decimal places).
If the critical angle for this glass is 42°, explain what will happen to a ray inside the glass that strikes the glass–air boundary at 40°, then at 45°.
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(a) Angle of refraction r = sin⁻¹(sin 45° / 1.5) = sin⁻¹(0.7071 / 1.5) ≈ 28.1° degree
(b) At 40° (less than the critical angle), the ray is mostly refracted out into the air with some weak reflection. At 45° (greater than critical), all light is reflected inside the glass—total internal reflection occurs.
Common mistakes: Forgetting to use sin values for angles; Wrong reasoning for total internal reflection
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Marking points
B1 (a) · 1 mark · Correct use of Snell’s Law (n = sin i / sin r). Substitutes values correctly.
B2 (a) · 1 mark · Accurately calculates angle of refraction (acceptable range: 27.9°–28.3°). (follow-through)
B3 (b) · 1 mark · States that at 40° the ray is refracted (and weak reflection).
B4 (b) · 1 mark · States that at 45° total internal reflection occurs.
B5 (b) · 1 mark · Links critical angle to whether refraction or reflection occurs clearly.
Worked solution
b) At 40°, since it's less than the critical angle, some light leaves the glass (refraction), some small amount reflects. At 45°, more than the critical angle, all light is reflected inside (total internal reflection).