Refraction at a plane surface — AQA A-Level Physics

Refraction at a plane surface is a fundamental topic in AQA A-Level Physics that explains how light changes direction when it passes from one medium to another. It introduces the refractive index, Snell's law, and the conditions for total internal reflection, which are essential for understanding lenses, optical fibres, and many real-world applications. You will learn to calculate angles of refraction, critical angles, and speeds of light in different materials.

This topic builds directly on your knowledge of waves and ray diagrams from GCSE and provides the foundation for more advanced topics such as lenses, diffraction, and polarisation. It is also heavily examined in both AS and A-Level papers, often combined with practical skills like drawing ray diagrams and using Snell's law in experiments. Mastering refraction is crucial for achieving high marks in waves and optics questions.

• →Refractive index n of a medium is defined as n = c / v, where c is the speed of light in a vacuum and v is the speed of light in the medium. It is always greater than or equal to 1.
• →Snell's law relates the angles of incidence and refraction to the refractive indices of the two media: n1 sin(theta1) = n2 sin(theta2), where angles are measured from the normal.
• →When light travels from a denser to a less dense medium, there is a critical angle C given by sin C = 1/n (for the denser medium relative to the less dense one). At angles greater than C, total internal reflection occurs.
• →The frequency of light remains constant during refraction, but its speed and wavelength change. The colour (frequency) does not change, but the wavelength changes according to v = f lambda.
• →Ray diagrams for refraction at a plane surface must show the normal, incident ray, refracted ray, and angles measured from the normal. For a parallel-sided block, the emergent ray is parallel to the incident ray but laterally displaced.

• A step-index fibre consists of a core of higher refractive index surrounded by cladding of lower refractive index, with an abrupt change of index at the core–cladding boundary.
• Total internal reflection occurs at the core–cladding boundary when light meets it at an angle of incidence greater than the critical angle, so light is repeatedly reflected along the core.
• The critical angle is related to the refractive indices by sin C = n₂ / n₁, where n₁ is the core index and n₂ is the cladding index, and n₁ must exceed n₂ for guidance to be possible.
• The acceptance angle at the entrance face determines whether an incoming ray can be guided; rays entering too steeply are refracted out through the cladding rather than trapped.
• Cladding protects the core surface, reduces scattering losses and prevents light crossing between adjacent fibres, while the buffer provides mechanical protection.
• Only step-index behaviour is required: the index changes sharply at one boundary, unlike graded-index fibres where the index varies continuously and rays follow curved paths.
• Material dispersion occurs because the refractive index of the core varies with wavelength, so different wavelengths travel at different speeds and spread out in time.
• Modal dispersion occurs because rays follow different zig-zag paths of different lengths in a step-index core, so they take different times to reach the far end.
• Both effects broaden an input pulse, causing adjacent pulses to overlap and limiting the maximum reliable bit rate over a given length of fibre.
• Using a monochromatic source such as a laser reduces material dispersion because the range of wavelengths present is very small.
• Reducing the core diameter or using a single-mode fibre reduces modal dispersion because fewer ray paths are available.
• Material and modal dispersion are separate mechanisms: one depends on wavelength spread, the other on path-length spread, and both can occur together in a step-index fibre.
• Pulse broadening is the temporal spreading of a signal pulse as it propagates, so the output pulse has a longer duration than the input pulse.
• Modal dispersion arises because rays travelling different paths in a multimode fibre have different path lengths and therefore different transit times.
• Material dispersion arises because the refractive index of the fibre depends on wavelength, so different spectral components travel at different speeds.
• Consequences of broadening include overlap of adjacent pulses, which limits the maximum bit rate and can cause detection errors.
• Absorption is the loss of optical power as light is absorbed by the fibre material or impurities, converting energy to other forms such as thermal energy.
• Absorption reduces signal amplitude, so the signal must be amplified or regenerated, and it limits the maximum transmission distance between repeaters.
• Using a monomode fibre reduces modal dispersion because only one mode propagates, and choosing a wavelength with low absorption reduces loss.

• 💡Draw a labelled longitudinal section showing core, cladding, buffer, the normal at the boundary and the zig-zag ray path, marking angles of incidence and reflection.
• 💡When calculating the critical angle, identify clearly which refractive index is n₁ and which is n₂ before substituting into sin C = n₂ / n₁.
• 💡Link the refractive index difference to the size of the critical angle: a larger difference gives a smaller critical angle and traps a wider range of rays.
• 💡Use a sketch of two rays with different path lengths to show how modal dispersion delays one ray relative to another.
• 💡When comparing the two effects, state the cause, the quantity that varies and the consequence for pulse arrival time in each case.
• 💡Link pulse broadening to bit rate by explaining that overlapping pulses make it impossible to distinguish successive bits reliably.
• 💡When explaining pulse broadening, refer explicitly to the effect on the output pulse duration and how that affects the ability to distinguish adjacent bits.
• 💡Use a labelled diagram or ray paths to show a short axial path and a longer zig-zag path in a multimode fibre, then state which arrives first.
• 💡For absorption, distinguish between the cause (energy absorbed by the material) and the consequence (reduced amplitude and need for amplification or regeneration).
• 💡Always draw the normal as a dashed line perpendicular to the surface and measure angles from it. Label angles clearly with the correct symbols (i, r, C).
• 💡When using Snell's law, write the full equation n1 sin(theta1) = n2 sin(theta2) before substituting numbers. This shows your method and can earn method marks even if the final answer is wrong.
• 💡For total internal reflection questions, always state the direction of travel (e.g., 'from glass to air') and compare the angle of incidence to the critical angle. Use the phrase 'angle of incidence is greater than the critical angle' to secure the mark.

• Thinking total internal reflection happens at the outer surface of the cladding rather than at the core–cladding boundary; correct this by stating that reflection occurs where the refractive index changes, at the core–cladding interface.
• Believing any ray entering the fibre will be trapped; correct this by explaining that the ray must strike the boundary above the critical angle, which requires entry within the acceptance angle.
• Confusing step-index with graded-index behaviour by describing a gradual change of refractive index; correct this by stating that in a step-index fibre the core index is uniform and changes abruptly at the cladding.
• Treating material and modal dispersion as the same effect; correct this by stating that material dispersion depends on wavelength-dependent refractive index while modal dispersion depends on different path lengths.
• Claiming that modal dispersion is reduced by using a brighter source; correct this by explaining that reducing the number of available paths, for example with a narrower core, is what reduces modal dispersion.
• Assuming a monochromatic source removes all dispersion; correct this by stating that it removes material dispersion but modal dispersion can still occur in a step-index fibre.
• Confusing pulse broadening with absorption: broadening changes pulse duration, whereas absorption reduces pulse amplitude. Correction: state that broadening is temporal spreading and absorption is energy loss.
• Thinking that all rays in a fibre travel at the same speed regardless of path: in a multimode fibre, rays with longer paths take longer, causing modal dispersion. Correction: link path length differences to arrival time differences.
• Assuming absorption is independent of wavelength: absorption varies with wavelength and material. Correction: refer to low-absorption wavelength windows when explaining how loss is minimised.
• Students often think that light bends because it hits the surface at an angle, but the real reason is the change in speed as it enters a different medium. Correction: Refraction occurs because the speed of light changes, causing the wavefront to change direction.
• Many believe that total internal reflection can happen when light travels from air into glass. Correction: Total internal reflection only occurs when light travels from a denser medium to a less dense medium (e.g., glass to air) and the angle of incidence exceeds the critical angle.
• Students sometimes think that the frequency of light changes during refraction. Correction: The frequency remains constant; only the speed and wavelength change. This is why the colour of light does not change upon refraction.

1. 1Day 1-2: Revise the definitions of refractive index and Snell's law. Practice calculating refractive index and angles using past paper questions. Ensure you can rearrange the formula confidently.
2. 2Day 3-4: Learn the conditions for total internal reflection and the critical angle formula. Practice drawing ray diagrams for semicircular blocks and optical fibres. Complete at least five calculations for critical angle.
3. 3Day 5-6: Work through exam-style questions on refraction at plane surfaces, including those with parallel-sided blocks and real-life applications. Focus on explaining why light bends and the effects on speed and wavelength.
4. 4Day 7: Create a summary sheet with key formulas, definitions, and common pitfalls. Test yourself with active recall prompts and past paper questions under timed conditions.
5. 5Day 8-10: Review any weak areas by re-reading textbook sections and watching video tutorials. Attempt a full past paper question on waves and optics to integrate your knowledge.

• 📋Calculation of refractive index or angle of refraction using Snell's law. Advice: Always write the formula, substitute values, and give your answer to an appropriate number of significant figures (usually 2 or 3).
• 📋Determination of critical angle and explanation of total internal reflection. Advice: State the direction of travel, use sin C = 1/n, and compare the angle of incidence to the critical angle in your explanation.
• 📋Ray diagram drawing for a light ray passing through a parallel-sided glass block or optical fibre. Advice: Use a ruler, draw the normal at each boundary, and ensure the emergent ray is parallel to the incident ray for a parallel-sided block.
• 📋Practical-based question on measuring refractive index using a glass block and ray tracing. Advice: Describe the procedure clearly, including how to measure angles and reduce errors, and include a suitable graph (e.g., sin i vs sin r) to determine n.