AQA A-Level Physics: Fibre Optics in Medical Physics — mark scheme explained

The question

A glass fibre has a core with a refractive index of 1.50 and a cladding with a refractive index of 1.46. Calculate the critical angle for total internal reflection at the core-cladding interface. [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 to find the critical angle: sin(θ c ) = n 2 / n 1

• S2

  Substitute the given values: sin(θ c ) = 1.46 / 1.50

• S3

  Calculate the critical angle: θ c = arcsin(1.46 / 1.50) ≈ 76.7°

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Use Snell's Law to find the critical angle: sin(θ c ) = n 2 / n 1

2. S2

   Substitute the given values: sin(θ c ) = 1.46 / 1.50

3. S3

   Calculate the critical angle: θ c = arcsin(1.46 / 1.50) ≈ 76.7°

4. Final answer: The critical angle for total internal reflection at the core-cladding interface is approximately 76.7°.

Common mistakes

• Confusing the roles of coherent and non-coherent fibre bundles. — Remember that coherent fibre bundles are used for image transmission because they maintain the spatial arrangement of light, while non-coherent fibre bundles are used for illumination and do not need to maintain a specific spatial arrangement.
• Forgetting to mention the critical angle in TIR calculations. — Always include the calculation of the critical angle using Snell's Law: sin(θ c ) = n 2 / n 1 .
• Not explaining how TIR ensures light transmission through the fibre. — Explain that total internal reflection occurs at the core-cladding interface when the angle of incidence exceeds the critical angle, ensuring that light is guided along the fibre.
• Confusing the refractive indices of the core and cladding. — Remember that the core has a higher refractive index (n 1 ) than the cladding (n 2 ) to ensure TIR occurs.
• Forgetting to mention the jacket in the structure of an optical fibre. — Always include the jacket as part of the fibre's structure, noting that it provides physical protection to the fibre.
• Not discussing the advantages of using fibre optics in medical imaging. — List and explain at least three advantages, such as minimally invasive procedures, high image quality, and flexibility.

Where the marks go

• Full worked solution (all marking points)3 marks

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