Fibre optics and endoscopy (A-level only) — AQA A-Level Physics

This topic explores how light can be guided along transparent fibres using total internal reflection, a phenomenon that occurs when light strikes a boundary at an angle greater than the critical angle. You will learn about the structure of optical fibres, including the core and cladding, and how they are used in telecommunications and medical endoscopy. The physics underpins modern high-speed internet and minimally invasive surgery.

In the AQA A-Level specification, this topic sits within the 'Waves and Optics' section, building on your understanding of refraction, reflection, and the critical angle. It also connects to practical applications, such as calculating numerical aperture and explaining signal degradation. Mastery of this topic is essential for exam questions that test both conceptual understanding and quantitative problem-solving.

• →Total internal reflection occurs when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle, given by sin C = n2/n1.
• →Optical fibres consist of a core with higher refractive index surrounded by cladding with lower refractive index, ensuring total internal reflection at the boundary.
• →Step-index fibres have a sharp change in refractive index, while graded-index fibres have a gradual change that reduces modal dispersion.
• →Endoscopes use two fibre bundles: a non-coherent bundle for illumination and a coherent bundle for imaging, where the spatial arrangement of fibres is preserved.
• →Signal degradation in fibres can occur due to absorption, scattering, and dispersion, which limit the maximum transmission distance and bandwidth.

• Total internal reflection occurs when light travels from a medium of higher refractive index to one of lower refractive index and the angle of incidence exceeds the critical angle.
• The critical angle C is given by sin C = n_cladding / n_core, where n_core > n_cladding.
• Light must enter the fibre within the acceptance angle so that it strikes the core–cladding boundary at an angle greater than C.
• At each TIR, the angle of reflection equals the angle of incidence and the light remains inside the core, so the signal can travel along a curved fibre.
• In medical physics, fibre optics allow illumination and imaging inside the body, for example in endoscopes, with reduced need for open surgery.
• A flexible endoscope uses fibre bundles to guide light into the body for illumination and to carry light out for imaging.
• A coherent bundle preserves the relative positions of fibres at both ends, so it can transmit an image.
• A non-coherent bundle has fibres in random relative positions, so it transmits light but not a spatially resolved image.
• An objective lens at the distal end forms an image on the bundle face, and a viewing lens or camera at the proximal end allows the image to be seen.
• Endoscopes enable internal imaging, for example of the gastrointestinal tract, with advantages such as flexibility, reduced invasiveness and real-time observation.

• 💡Sketch the core and cladding, mark the normal at the interface, and label the angle of incidence and the reflected ray to show TIR clearly.
• 💡When calculating the critical angle, state the refractive indices used and check that the value is less than 90°.
• 💡Link each property of the fibre to a medical use, such as flexible bundles for imaging or illumination during endoscopy.
• 💡Use a labelled diagram to show the light path: illumination bundle, object, objective lens, coherent image bundle and viewing end.
• 💡When comparing bundle types, state clearly whether relative fibre positions are preserved and link this to image formation.
• 💡Give a named medical example, such as gastroscopy or colonoscopy, and state one advantage such as flexibility or reduced recovery time.
• 💡Always define the critical angle and state the conditions for total internal reflection clearly; examiners look for the direction of travel and the angle condition.
• 💡When calculating the critical angle, ensure you use the correct refractive indices and rearrange the formula sin C = n2/n1 correctly.
• 💡In endoscopy questions, explicitly mention the role of the coherent bundle and how it preserves the image; vague answers lose marks.

• Thinking that TIR can happen when light travels from a lower to a higher refractive index; correction: TIR requires travel from higher to lower refractive index, as from core to cladding.
• Using sin C = n_core / n_cladding; correction: for core-to-cladding TIR, sin C = n_cladding / n_core.
• Believing that any ray entering the fibre will be trapped; correction: the ray must enter within the acceptance angle so that it meets the interface above the critical angle.
• Confusing coherent and non-coherent bundles; correction: coherent bundles preserve fibre order and can carry an image, while non-coherent bundles cannot.
• Thinking that a single fibre can produce a full image; correction: an image requires many fibres in a coherent bundle, each carrying part of the image.
• Assuming the endoscope only illuminates and does not image; correction: separate bundles or channels are used for illumination and for image transmission.
• Students often think total internal reflection occurs when light travels from less dense to denser medium. Correction: It only occurs from denser to less dense, with angle of incidence > critical angle.
• Students may believe that a single fibre can both illuminate and carry an image in an endoscope. Correction: Two separate bundles are needed: one non-coherent for light delivery and one coherent for image retrieval.
• Students sometimes assume that light travels in a straight line down the fibre. Correction: Light undergoes multiple total internal reflections, zigzagging along the fibre.

1. 1Day 1-2: Review the principles of refraction and total internal reflection, including the derivation of sin C = n2/n1. Practice calculations of critical angle for different media.
2. 2Day 3-4: Study the structure and function of optical fibres, including core, cladding, and the difference between step-index and graded-index fibres. Learn about modal dispersion.
3. 3Day 5-6: Explore the application of fibre optics in endoscopy. Understand the difference between coherent and non-coherent bundles and how images are formed.
4. 4Day 7-8: Work through past exam questions on fibre optics and endoscopy, focusing on 6-mark explanation questions and calculations. Review mark schemes to identify key terminology.
5. 5Day 9-10: Create a summary mind map linking total internal reflection, fibre structure, and endoscopy. Test yourself with active recall prompts and practice explaining concepts aloud.

• 📋Calculation of critical angle or refractive index using sin C = n2/n1. Advice: Show all steps and give answers to appropriate significant figures.
• 📋Explanation of how total internal reflection allows light to propagate in an optical fibre. Advice: Include the conditions and refer to core and cladding.
• 📋Description of the structure and function of an endoscope, including the role of coherent and non-coherent bundles. Advice: Use clear diagrams and label the bundles.
• 📋Discussion of advantages and limitations of fibre optics in medicine or communications. Advice: Link to signal degradation, flexibility, and minimally invasive procedures.