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
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculations, show all steps clearly and include units in your final answer. For explanations and descriptions, use key physics terms and provide clear, concise answers. Always check your work for any errors or omissions.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Explain
- Provide a detailed account of how or why something happens, using appropriate physics concepts and terminology.
- Describe
- Give a clear and concise account of the features or characteristics of something.
- Determine
- Find out or establish a particular value or quantity by calculation or measurement.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes per question to ensure you have enough time to read the question carefully, perform calculations, and write a well-structured answer.
- Use Snell's law: n 1 sin θ 1 = n 2 sin θ 21 mark
- Substitute the given values: 1 × sin 30° = 1.5 × sin θ 21 mark
- Calculate sin 30°: sin 30° = 0.51 mark
- Rearrange to solve for sin θ 2 : sin θ 2 = (0.5) / 1.5 ≈ 0.3331 mark
- Find the angle of refraction: θ 2 = arcsin(0.333) ≈ 19.47°1 mark
Final answer: The angle of refraction is approximately 19.47°.
Work through every step correctly and you earn all 5 marks.
Another worked example
A light ray travels from a medium with refractive index 1.6 into air (n = 1). Calculate the critical angle for total internal reflection.
- Use the formula for the critical angle: sin θ c = n 2 / n 11 mark
- Substitute the given values: sin θ c = 1 / 1.61 mark
- Calculate sin θ c : sin θ c ≈ 0.6251 mark
- Find the critical angle: θ c = arcsin(0.625) ≈ 38.68°1 mark
Final answer: The critical angle for total internal reflection is approximately 38.68°.
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing the refractive index with the speed of light in a medium
Why it happens: Students sometimes mix up the definitions and use the speed of light instead of the refractive index in calculations.
Fix: 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
Why it happens: Students often use the angle between the ray and the boundary instead of the angle with the normal.
Fix: 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
Why it happens: Students sometimes forget that Snell's law involves the sine of the angles, not the angles themselves.
Fix: 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
Why it happens: Students sometimes think that any angle greater than 45° will result in total internal reflection, regardless of the refractive indices.
Fix: 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
Why it happens: Students often mix up the causes of pulse broadening in optical fibres.
Fix: 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
Why it happens: Students sometimes use a more precise value for the refractive index of air, which can complicate calculations unnecessarily.
Fix: Always use the approximate value of 1 for the refractive index of air unless otherwise specified.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Apply Snell's Law | Use Snell's law to find the refraction angle from given refractive indices and incidence angle. | 5 |
| Calculate Critical Angle | Use the critical angle formula with the two refractive indices to find the angle. | 4 |
| Calculate Critical Angle | Use the two refractive indices to find the critical angle at the core–cladding boundary. | 5 |
| Calculate Pulse Broadening | Multiply the dispersion per kilometre by the fibre length to find total broadening. | 3 |
| Total across these question types | 17 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.