AQA A-Level Physics Paper 1, June 2025: Question 18

1 mark · Medium difficulty · Multiple Choice

Calculate the refractive index of medium Y given the angles of an incident and refracted light ray relative to the boundary and the refractive index of medium X.

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Question

Diagram showing a light ray passing across a vertical boundary from medium X on the left to medium Y on the right. In medium X, the ray approaches the boundary from the lower-left, making an angle of 145° with the upper boundary line. In medium Y, the refracted ray continues into the upper-right, making an angle of 62° with the upper boundary line. The refractive index of medium X is given as 1.33. Four multiple-choice options are provided for the refractive index of medium Y: A: 0.86, B: 1.22, C: 1.74, D: 2.32.
Question text

18 A light ray passes from medium X to medium Y.

The refractive index of X is 1.33

What is the refractive index of Y?

[1 mark]

A 0.86

B 1.22

C 1.74

D 2.32

Mark scheme

Show the mark scheme Mark scheme table row for question 18 showing the correct key as 'D', the answer value as '2.32', and the assessment objective as 'AO2'.

18 D 2.32 AO2

How to answer it

Refraction at a Boundary: Snell's Law & Angles to the Normal

📋 What this question tests

This question assesses your ability to apply Snell's Law of Refraction ( n₁ sin θ₁ = n₂ sin θ₂ ) to find an unknown refractive index. Crucially, it tests geometric awareness: recognising that angles in Snell's law are measured relative to the normal (perpendicular) to the interface, rather than the boundary line itself.

Question 18 Walkthrough

Multiple Choice (1 Mark) — AO2 (Application of Knowledge)

✅ Correct Answer

D (2.32)

Mark Scheme: Award 1 mark for Option D.

💡 Key Knowledge

  • Snell's Law: nX sin(θX) = nY sin(θY)
  • The Normal: Always perpendicular (90°) to the boundary line between the two media.
  • Because the interface is a vertical line, the normal is a horizontal line drawn through the point of incidence.
  • Angles of incidence and refraction must always be measured from the ray to the normal.

📐 Step-by-Step Calculation

  1. Identify the boundary and normal:
    The boundary is the vertical line separating Medium X and Medium Y. Therefore, the normal is horizontal (at 90° to the vertical interface).
  2. Find angle of incidence in medium X (θX):
    The given angle from the upper vertical interface down to the incident ray is 145°.
    The normal lies at 90° from the vertical interface.
    θX = 145° − 90° = 55°
    (Alternatively: the angle to the lower boundary is 180° − 145° = 35°, so to the normal: 90° − 35° = 55°).
  3. Find angle of refraction in medium Y (θY):
    The given angle between the upper vertical interface and the refracted ray is 62°.
    Since the normal is at 90° to the interface:
    θY = 90° − 62° = 28°
  4. Apply Snell's Law to calculate nY:
    nX sin(θX) = nY sin(θY)
    1.33 × sin(55°) = nY × sin(28°)
    1.33 × 0.8192 = nY × 0.4695
    1.0895 = nY × 0.4695
    nY = 1.0895 / 0.4695 = 2.3206... ≈ 2.32

❌ Common Errors & Distractor Traps

  • Mistaking the vertical boundary for the normal:
    Using 35° (or 145°) and 62° directly gives n = 1.33 × sin(35°) / sin(62°) = 0.86 (leads directly to Distractor A).
  • Converting only one angle:
    Correctly finding θX = 55° but using the given 62° directly for Y gives n = 1.33 × sin(55°) / sin(62°) = 1.22 (leads directly to Distractor B).
  • Inverting the Snell's ratio:
    Dividing the wrong way gives values < 1, which should immediately raise suspicion since the ray bends towards the normal (meaning medium Y must be optically denser, so nY > nX ).

🧠 Exam Technique & Sanity Checks

  • Sketch the normal first: Always draw a dashed line perpendicular to the interface before touching your calculator.
  • Qualitative check: Notice the ray bends towards the normal as it enters Y ( 55° → 28° ). That means light slows down, so medium Y must have a higher refractive index than 1.33.
  • This immediately eliminates A (0.86) and B (1.22) without any calculation!

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.