Electromagnetic waves — OCR A-Level Physics
Test yourself on Electromagnetic waves with OCR A-Level practice questions.
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Electromagnetic waves explained
The electromagnetic spectrum is the continuous family of transverse waves that propagate through a vacuum at the speed of light, c = 3.00 × 10⁸ m s⁻¹.
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Its regions, in order of increasing frequency and decreasing wavelength, are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. All electromagnetic waves share key properties: they are transverse, can travel through a vacuum, transfer energy, and show reflection, refraction, diffraction, interference and polarisation. They differ in wavelength, frequency, photon energy and typical interaction with matter. In an MCQ, you may be asked to order regions, identify a shared property, or distinguish electromagnetic waves from mechanical waves such as sound, which need a medium.
(b) orders of magnitude of wavelengths of the principal radiations from radio waves to gamma rays
You need approximate orders of magnitude for the wavelength of each principal region. Radio waves extend from about 10⁻¹ m to 10⁴ m or more; microwaves about 10⁻³ m to 10⁻¹ m; infrared about 7 × 10⁻⁷ m to 10⁻³ m; visible light about 4 × 10⁻⁷ m to 7 × 10⁻⁷ m; ultraviolet about 10⁻⁸ m to 4 × 10⁻⁷ m; X-rays about 10⁻¹¹ m to 10⁻⁸ m; gamma rays shorter than about 10⁻¹¹ m. These are orders of magnitude, not sharp boundaries, and regions overlap slightly. In an MCQ you may be asked which region has a wavelength of a given order, or to place a value in the correct region.
(c) plane polarised waves; polarisation of electromagnetic waves
A plane polarised wave has oscillations confined to a single plane. For an electromagnetic wave, the electric field vector oscillates in one specific plane containing the direction of propagation. Unpolarised light features electric field oscillations in multiple planes perpendicular to the direction of travel. Polarisation can be achieved by passing light through a polarising filter, which transmits only the component of the electric field aligned with its transmission axis. If unpolarised light passes through a polariser, the transmitted intensity is halved. When this polarised light of intensity I₀ strikes a second filter (an analyser), the transmitted intensity I is given by Malus's law: I = I₀ cos²θ, where θ is the angle between the transmission axes. Polarisation provides crucial evidence that electromagnetic waves are transverse.
(d)
This printed “(d)” is a structural parent label rather than a standalone learning outcome. Its assessable content is carried by the two following subclauses: (i) refraction, refractive index, n = c/v and n sin i = constant at a boundary; and (ii) the ray-box techniques used to investigate refraction and total internal reflection with rectangular and semi-circular blocks. Use the complete child rows when studying or practising these ideas. Do not treat the bare label as a separate physics fact or confuse it with the later standalone outcome (e), which defines the critical angle and total internal reflection.
(i) refraction of light; refractive index; n = c/v; n sin i = constant at a boundary where i is the angle to the normal
Refraction is the change in direction of light when it crosses a boundary between media, caused by a change in speed. The refractive index n of a medium is defined by n = c/v, where c is the speed of light in a vacuum (3.00 × 10⁸ m s⁻¹) and v is the speed in the medium; n is dimensionless and always ≥ 1. At a boundary, n sin i is constant, where i is measured from the normal, not the surface. For light going from medium 1 to medium 2, n₁ sin i₁ = n₂ sin i₂. Example: light entering glass (n = 1.50) from air at i = 30.0° gives sin r = sin 30.0°/1.50 = 0.333, so r = 19.5°. A larger n means greater bending towards the normal on entry.
(ii) techniques and procedures used to investigate refraction and total internal reflection of light using ray boxes, including transparent rectangular and semi-circular blocks
A ray box produces a narrow beam of light to investigate refraction and total internal reflection (TIR). For a rectangular block, trace the incident, internal, and emergent rays, measuring angles of incidence and refraction from the normal to verify Snell's law. For a semi-circular block, direct the ray into the curved face along a radius so it hits the exact centre of the flat face. Because it enters along the normal to the curved surface, it passes undeviated. At the flat face, the ray refracts out. By rotating the block to increase the angle of incidence at the flat face, the refracted ray eventually grazes the boundary; this is the critical angle. Further rotation results in TIR. Repeat measurements to reduce random error.
(e) critical angle; sin C = 1/n; total internal reflection for light.
When light travels from a denser medium of refractive index n towards a less dense medium such as air, the angle of refraction is larger than the angle of incidence. At the critical angle C, the refracted ray emerges along the boundary at 90° to the normal, so n sin C = 1 × sin 90° = 1, giving sin C = 1/n. For angles of incidence greater than C, no light refracts out; it is all reflected back inside the medium, which is total internal reflection. Example: for glass with n = 1.50, sin C = 1/1.50 = 0.667, so C = 41.8°. Total internal reflection requires the light to be travelling towards a less optically dense medium and i > C.
Your focus
- List the regions of the electromagnetic spectrum in order of wavelength or frequency.
- Describe the shared properties of all electromagnetic waves.
- Use c = fλ to relate frequency and wavelength for any region.
Show all 21 objectives
- Recall approximate wavelength ranges for each principal region.
- Assign a given wavelength to the correct region of the spectrum.
- Convert between metres and prefixed units such as nanometres and picometres.
- Define plane polarised electromagnetic waves in terms of the electric field oscillation plane.
- Explain how polarising filters produce polarised light from an unpolarised source.
- Calculate transmitted intensity using Malus's law, correctly identifying the incident polarised intensity.
- Identify that the bare “(d)” row is a structural parent and has no standalone assessable wording.
- Locate the complete assessable content in child rows (i) and (ii).
- Distinguish the child refraction and practical outcomes from the separate critical-angle outcome (e).
- Define refractive index using n = c/v and explain why it is dimensionless.
- Apply n₁ sin i₁ = n₂ sin i₂ to find an unknown angle at a boundary.
- Predict the direction of bending when light moves between media of different refractive index.
- Describe how to use a ray box and rectangular block to investigate refraction and measure angles from the normal.
- Explain the correct procedure for using a semi-circular block to observe total internal reflection at the flat face.
- Identify the critical angle experimentally by finding the angle of incidence that produces a 90-degree angle of refraction.
- Define the critical angle and derive sin C = 1/n from the boundary equation.
- Calculate the critical angle for a given refractive index.
- Explain the two conditions required for total internal reflection to occur.
Electromagnetic waves exam tips
Marking Points
- Electromagnetic waves are transverse oscillations of electric and magnetic fields and do not require a medium.
- All regions travel through a vacuum at c = 3.00 × 10⁸ m s⁻¹.
- The spectrum order from longest to shortest wavelength is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
- Frequency and wavelength are inversely related through c = fλ, so increasing frequency means decreasing wavelength.
- All regions can be reflected, refracted, diffracted, interfere and be polarised.
- Regions differ in photon energy E = hf and in how they interact with matter.
- Radio waves: roughly 10⁻¹ m to 10⁴ m and beyond.
- Microwaves: roughly 10⁻³ m to 10⁻¹ m.
- Infrared: roughly 10⁻⁷ m to 10⁻³ m.
- Visible light: roughly 4 × 10⁻⁷ m to 7 × 10⁻⁷ m.
- Ultraviolet: roughly 10⁻⁸ m to 4 × 10⁻⁷ m.
- X-rays: roughly 10⁻¹¹ m to 10⁻⁸ m.
- Gamma rays: shorter than about 10⁻¹¹ m.
- Defines a plane polarised wave as one where oscillations are confined to a single plane.
- States that for electromagnetic waves, the electric field vector oscillates in a single plane containing the direction of propagation.
- Explains that unpolarised light has electric field oscillations in many planes perpendicular to the direction of travel.
- Applies Malus's law (I = I₀ cos²θ) correctly, identifying I₀ as the maximum intensity of the polarised light incident on the analyser.
- Concludes that the ability to be polarised is evidence that electromagnetic waves are transverse.
- Refraction is the change in direction of a wave at a boundary due to a change in speed in the new medium.
- Refractive index is defined as n = c/v, the ratio of the speed of light in a vacuum to its speed in the medium.
- n is dimensionless and has a value greater than or equal to 1 for a material medium.
- The general boundary relationship is n₁ sin i₁ = n₂ sin i₂, with angles measured from the normal.
- For light entering a denser medium (larger n), the ray bends towards the normal; leaving it, the ray bends away.
- A typical calculation: sin r = sin i/n, e.g. sin r = sin 30.0°/1.50 = 0.333 giving r = 19.5°.
- Use a ray box to produce a narrow beam and trace rays entering and exiting a rectangular block to investigate refraction.
- Measure angles of incidence and refraction from the normal drawn at the boundary of the rectangular block.
- For a semi-circular block, direct the incident ray through the curved face towards the centre of the flat face so it enters undeviated.
- Observe refraction at the flat face and increase the angle of incidence until the emergent ray grazes the flat boundary to find the critical angle.
- Increase the angle of incidence beyond the critical angle to observe total internal reflection at the flat face.
- The critical angle C is the angle of incidence in the denser medium for which the angle of refraction is 90°.
- At the critical angle, n sin C = 1, so sin C = 1/n where n is the refractive index of the denser medium relative to the less dense medium.
- Total internal reflection occurs when light travels towards a less optically dense medium and the angle of incidence exceeds C.
- At i > C no light is refracted out of the medium; all the light is reflected internally.
- Example: for n = 1.50, sin C = 1/1.50 = 0.667, so C = 41.8°.
- Total internal reflection cannot occur when light travels from a less dense to a denser medium.
Examiner Tips
- 💡Learn the spectrum order as a sequence and check whether the question asks for increasing frequency or increasing wavelength.
- 💡Use c = fλ to convert between wavelength and frequency rather than memorising separate values.
- 💡Eliminate options that claim electromagnetic waves are longitudinal or need a medium.
- 💡Check units and powers of ten carefully when comparing wavelengths.
- 💡Anchor visible light at about 5 × 10⁻⁷ m and work outwards in powers of ten.
- 💡Compare the exponent first, then the coefficient, when judging which region a wavelength belongs to.
- 💡Remember that shorter wavelength means higher frequency and higher photon energy.
- 💡Watch for values given in nanometres or picometres and convert to metres before comparing.
- 💡When dealing with two filters, remember to halve the intensity of unpolarised light through the first polariser before applying Malus's law for the second.
- 💡Sketch the planes of oscillation to help visualise the effect of polarising filters.
- 💡Explicitly link the phenomenon of polarisation to the transverse nature of electromagnetic waves in explanation questions.
- 💡Revise subclause (i) for the refraction definitions and equations, including angles measured from the normal.
- 💡Revise subclause (ii) for the rectangular- and semi-circular-block experimental procedures.
- 💡Use outcome (e) when practising critical-angle calculations and the conditions for total internal reflection.
- 💡Sketch the normal as a dashed line at 90° to the surface before marking any angle.
- 💡Check that your calculated r is smaller than i when light enters a higher-n medium.
- 💡Keep speeds in m s⁻¹ and use c = 3.00 × 10⁸ m s⁻¹ consistently in n = c/v.
- 💡Clearly describe aiming the ray at the centre of the flat face through the curved side when explaining the semi-circular block experiment.
- 💡State that repeating the experiment for various angles of incidence and calculating a mean reduces random error.
- 💡Remember to mention using a sharp pencil to mark the centre of the ray to improve the precision of angle measurements.
- 💡Check that n > 1 before using sin C = 1/n; if n < 1 you have inverted the ratio.
- 💡State both conditions for total internal reflection: denser-to-less-dense direction and i > C.
- 💡Give C to a sensible number of significant figures, for example 41.8° for n = 1.50.
Common Mistakes
- Thinking electromagnetic waves need a medium: they propagate through a vacuum, unlike sound.
- Believing visible light is the only region that can be polarised: all electromagnetic waves can be polarised.
- Reversing the spectrum order: radio waves have the longest wavelength and gamma rays the shortest.
- Assuming all regions have the same photon energy: energy depends on frequency, so gamma photons carry far more energy than radio photons.
- Treating the boundaries as exact: they are orders of magnitude and adjacent regions overlap.
- Confusing infrared and ultraviolet ranges: infrared is longer than visible, ultraviolet shorter.
- Placing X-rays at longer wavelengths than ultraviolet: X-rays are shorter than ultraviolet.
- Forgetting that gamma rays have the shortest wavelengths, below about 10⁻¹¹ m.
- Using the initial unpolarised intensity as I₀ in Malus's law. Correction: I₀ is the intensity of the already polarised light incident on the analyser; the first polariser halves the unpolarised intensity.
- Stating that polarisation proves waves are electromagnetic. Correction: it proves they are transverse; other transverse waves can also be polarised.
- Believing a polarising filter blocks all light. Correction: it transmits the component of the electric field parallel to its transmission axis.
- Treating the bare “(d)” label as a complete learning outcome; the assessable detail is in its following subclauses (i) and (ii).
- Studying only the refraction equation and overlooking the required ray-box procedures in subclause (ii).
- Assigning the later critical-angle outcome (e) to this parent label; outcome (e) is a separate printed row.
- Measuring the angle from the boundary surface instead of the normal; the correction is that i and r are always angles between the ray and the normal.
- Writing n = v/c rather than n = c/v; the correction is that n compares the vacuum speed to the medium speed, so n ≥ 1.
- Assuming n sin i is constant for all boundaries regardless of the second medium; the correction is that n₁ sin i₁ = n₂ sin i₂ links the two specific media.
- Treating n as having units; the correction is that n is a dimensionless ratio of two speeds.
- Directing the ray into the flat face of the semi-circular block to find the critical angle: the ray must enter the curved face undeviated and undergo TIR at the flat face.
- Measuring angles from the surface of the block: always draw a normal line at the point of incidence and measure angles from the normal.
- Failing to aim the ray exactly at the centre of the flat face of the semi-circular block: this causes unwanted refraction at the curved boundary, invalidating the angle measurements.
- Using sin C = n instead of sin C = 1/n; the correction is that C is found from the reciprocal of n.
- Thinking total internal reflection can happen at any boundary; the correction is that light must be going from a denser to a less dense medium.
- Confusing the critical angle with the angle of refraction; the correction is that C is the angle of incidence in the denser medium when the refracted angle is 90°.
- Believing some light still refracts out at i > C; the correction is that beyond C all the light is internally reflected.