AQA AS Level Physics Paper 2, November 2021: Question 18

1 mark · Medium difficulty · Multiple Choice

Determine the angle of incidence of a light ray at the right-hand boundary of a rectangular glass block given the angle of refraction and refractive index.

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Question

A diagram shows a ray of light incident on the internal boundary of a rectangular glass block in air, refracting out into the air at an angle of 30 degrees to the normal, and reflecting inside the block towards a right-hand boundary. Below the diagram are four multiple-choice options A (20 degrees), B (42 degrees), C (48 degrees), and D (70 degrees).
Question text

18 A ray of light is incident on the internal boundary of a rectangular glass block in air.

Part of the light refracts out of the block at an angle of 30°.

Some of the remaining light reflects within the block to become incident on the right-hand

boundary.

refractive index of glass = 1.48

What is the angle of incidence of the ray at the right-hand boundary?

[1 mark]

A 20°

B 42°

C 48°

D 70°

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 18 is D, corresponding to an angle of 70 degrees.

18 D 70°

How to answer it

Optics: Refraction & Internal Reflection in a Glass Block

What this question tests

This question assesses your ability to apply Snell's Law of refraction, understand the relationship between angles of incidence and refraction at a boundary, and use basic geometry (angles on a straight line and alternate interior angles) to trace light paths through a rectangular block.

Question 18: Multiple Choice Analysis

Determining the angle of incidence at the right-hand boundary

✅ Correct Answer: D (70°)

The correct option is D. Following a step-by-step calculation using Snell's Law and block geometry yields an angle of incidence of 70° at the right-hand boundary.

Awarded 1 mark for selecting D.

💡 Key Knowledge

  • Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂)
  • For light entering air from glass, n_glass = 1.48 and n_air = 1.00.
  • Angles of incidence and refraction are always measured relative to the normal (perpendicular to the boundary).
  • The geometry of a rectangle means internal reflected angles correspond predictably with angles inside the block.

🧠 Exam Technique

Multi-step optics questions require working backwards from the given output. Break the problem into chronological milestones:

  1. Find the angle inside the glass at the bottom boundary.
  2. Use triangle or straight-line geometry to find the internal angle facing the right-hand boundary.

❌ Common Errors

  • Measuring from the surface: Using the 30° angle directly as the angle in air instead of measuring from the normal.
  • Inverting refractive indices: Forgetting which medium is 1 and which is 2 in Snell's Law.
  • Geometric slips: Subtracting angles from 90° incorrectly when transitioning from the bottom boundary to the side boundary.

📐 Step-by-Step Calculation

  1. Step 1: Calculate the angle of incidence at the bottom internal boundary.
    Using Snell's Law: n_glass sin(θ_glass) = n_air sin(θ_air)
    1.48 × sin(θ_glass) = 1.00 × sin(30°)
    sin(θ_glass) = sin(30°) / 1.48 = 0.5 / 1.48 ≈ 0.3378
    θ_glass = sin⁻¹(0.3378) ≈ 19.76°
  2. Step 2: Relate the transmitted angle to the internally reflected angle.
    By the law of reflection, the angle of reflection equals the angle of incidence (19.76°).
  3. Step 3: Determine the angle at the right-hand boundary.
    Looking at the triangle formed inside the glass block, the normal to the bottom surface is perpendicular (90°) to the surface, and the right-hand boundary is perpendicular to the bottom surface.
    The ray travels up toward the right-hand boundary. The complementary angle to the normal at the bottom is: 90° − 19.76° = 70.24°.
    Alternatively, considering the geometry of the normal at the right-hand boundary (which is horizontal):
    Angle of incidence at the right-hand boundary = 90° − 19.76° ≈ 70° (matching option D).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.