A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Refractive Index and Optical Fibres — mark scheme explained
The short answer
The refractive index of a substance is a fundamental concept in the study of waves, particularly light. It describes how much light slows down when it enters a medium from another.
The question
A light ray travels from air (n = 1) into a glass block (n = 1.5). If the angle of incidence is 30°, calculate the angle of refraction. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Use Snell's law: n 1 sin θ 1 = n 2 sin θ 2
- S2
Substitute the given values: 1 × sin 30° = 1.5 × sin θ 2
- S3
Calculate sin 30°: sin 30° = 0.5
- S4
Rearrange to solve for sin θ 2 : sin θ 2 = (0.5) / 1.5 ≈ 0.333
- S5
Find the angle of refraction: θ 2 = arcsin(0.333) ≈ 19.47°
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Use Snell's law: n 1 sin θ 1 = n 2 sin θ 2
- S2
Substitute the given values: 1 × sin 30° = 1.5 × sin θ 2
- S3
Calculate sin 30°: sin 30° = 0.5
- S4
Rearrange to solve for sin θ 2 : sin θ 2 = (0.5) / 1.5 ≈ 0.333
- S5
Find the angle of refraction: θ 2 = arcsin(0.333) ≈ 19.47°
Final answer: The angle of refraction is approximately 19.47°.
Common mistakes
- Confusing the refractive index with the speed of light in a medium — Always remember that the refractive index (n) is defined as n = c 0 / c s , where c 0 is the speed of light in a vacuum and c s is the speed of light in the substance.
- Using the wrong angles in Snell's law — Always measure the angles of incidence and refraction from the normal (a line perpendicular to the boundary) to the respective rays.
- Forgetting to use the sine function in Snell's law — Ensure you use the sine function when applying Snell's law: n 1 sin θ 1 = n 2 sin θ 2 .
- Misinterpreting the critical angle for total internal reflection — Calculate the critical angle using sin θ c = n 2 / n 1 , where n 1 is the higher refractive index and n 2 is the lower refractive index.
- Confusing material dispersion with modal dispersion — Material dispersion occurs due to different wavelengths traveling at slightly different speeds, while modal dispersion occurs in multi-mode fibres where different modes take different times to travel through the fibre.
- Forgetting that the refractive index of air is approximately 1 — Always use the approximate value of 1 for the refractive index of air unless otherwise specified.
Where the marks go
- Full worked solution (all marking points)5 marks