Wave nature of light

Learning goals

What students should be able to explain, calculate and investigate after completing Wave Nature of Light.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Categorise electromagnetic waves by wavelength, frequency, ionising ability and everyday use.
• Higher Level: Use the diffraction grating equation to calculate wavelength.
• Explain polarisation and how it demonstrates that light is a transverse wave.
• Explain dispersion of white light.
• Define solar irradiance and discuss its impact on life on Earth.

Key definitions

Precise terms, symbols and SI units used in Wave Nature of Light.

The Electromagnetic Spectrum

All electromagnetic waves travel at speed c in a vacuum; they differ in frequency and wavelength, and therefore in photon energy.

Higher-frequency electromagnetic waves carry more energy per photon (E = hf, from the Electron and Photoelectric Effect topic) and are generally more ionising and more hazardous to living tissue — X-rays and gamma rays are ionising radiation; higher-frequency ultraviolet can also be ionising, while lower-frequency ultraviolet, visible light, infrared, microwave and radio waves are generally non-ionising. Each region of the spectrum has characteristic everyday uses: radio (broadcasting, communications), microwave (cooking, satellite communication), infrared (thermal imaging, remote controls), visible light (human vision), ultraviolet (sterilisation, vitamin D production, but also skin damage), X-rays (medical imaging), and gamma rays (cancer treatment, sterilisation).

The Diffraction Grating

A diffraction grating has a very large number of closely spaced parallel slits.

Each narrow slit acts as a coherent source. Bright maxima occur at angles where light from adjacent slits travels an extra whole number of wavelengths, so the waves arrive in phase. A larger number of illuminated slits produces narrower, sharper principal maxima. Different wavelengths peak at different angles, allowing spectra to be measured.

• Gap much larger than wavelength → little spreading.
• Gap similar to wavelength → strong spreading.
• A diffraction grating uses many narrow, equally spaced openings. Their diffracted waves overlap and interfere, producing sharp principal maxima.

• From nλ = d sin θ, increasing wavelength λ increases the diffraction angle θ for the same order. Red light is therefore diffracted through a larger angle than violet light.
• Using a grating with more lines per millimetre makes the slit spacing d smaller. This increases the angular separation of the orders, but reduces the greatest possible order because |sin θ| cannot exceed 1.
• Moving the screen farther away increases the linear separation of the bright spots on the screen, but it does not change their diffraction angles.

Polarisation

Ordinary light consists of transverse waves vibrating in many different planes (all perpendicular to the direction of travel, but in every possible orientation around that direction).

The electric field in unpolarised light vibrates in many transverse directions. A polarising filter transmits the component along its transmission axis. Polarisation therefore provides evidence that light is transverse.

• Polarisation restricts wave oscillations to one plane.
• Only transverse waves can be polarised.
• A second polariser transmits maximum light when aligned and minimum light when crossed at 90°.

Dispersion

White light is a mixture of many different wavelengths (colours).

When white light enters a medium such as glass, each wavelength refracts by a very slightly different amount (the refractive index of a material depends slightly on wavelength) — violet light bends the most, red light the least. Passing white light through a prism therefore spreads it out into a visible spectrum of colours, a phenomenon called dispersion; the same underlying effect (water droplets acting like tiny prisms) produces a rainbow.

Solar Irradiance

Solar irradiance is the power of the Sun's electromagnetic radiation received per unit area at a given location: I = P/A.

It varies with factors including latitude, time of year, time of day, and atmospheric conditions (cloud cover, pollution). Solar irradiance is essential to life on Earth (driving photosynthesis, weather patterns, and the water cycle) and is also directly important for renewable energy: the amount of usable power a solar panel can generate depends directly on the solar irradiance falling on it.

Diagrams and formulae

Key diagrams and equations for reviewing Wave Nature of Light.

• The electromagnetic spectrum runs from radio waves (longest wavelength and lowest frequency) to gamma rays (shortest wavelength, highest frequency and highest photon energy).
• Diffraction grating: light passing through produces a central maximum and symmetric higher-order maxima at angles given by nλ = d sin θ.
• Dispersion: a prism splits white light into its component colours because each wavelength refracts by a slightly different amount.

The electromagnetic spectrum runs from radio waves (longest wavelength and lowest frequency) to gamma rays (shortest wavelength, highest frequency and highest photon energy).

Diffraction grating: light passing through produces a central maximum and symmetric higher-order maxima at angles given by nλ = d sin θ.

Dispersion: a prism splits white light into its component colours because each wavelength refracts by a slightly different amount.

• Key relationships
• Diffraction grating: nλ = d sin θ Wave speed of light: c = fλ

Worked Example

A step-by-step calculation applying the central relationships in Wave Nature of Light.

Light of wavelength 6 × 10⁻⁷ m falls on a diffraction grating with 500 lines per mm. Calculate the angle to the first-order maximum (n = 1).

• d = 1/(500 lines per mm) = 1/500 mm = 2 × 10⁻³ mm = 2 × 10⁻⁶ m
• nλ = d sin θ → sin θ = nλ/d = (1 × 6×10⁻⁷) ÷ (2×10⁻⁶) = 0.3
• θ = sin⁻¹(0.3) ≈ 17.5°

Practical / Investigation

Experimental planning, measurement and evaluation for Wave Nature of Light.

Experiment: Measuring the wavelength of laser light using a diffraction grating

• Apparatus: laser, diffraction grating (known lines per mm), screen, metre stick.
• Method: shine the laser through the grating onto a screen a measured distance away; measure the distance between the central maximum and the first-order maximum on the screen, and use trigonometry (with the grating-to-screen distance) to find the angle θ.
• Calculate the wavelength using λ = d sin θ / n.
• Sources of error: difficulty judging the exact centre of each bright spot; the grating not being exactly perpendicular to the laser beam.
• Improvement: measuring the distance between the +1 and −1 order maxima (on either side of the central spot) and halving it gives the distance to a single first-order maximum while reducing the error from trying to pinpoint the exact centre of the central spot; measure to the centre of several higher-order maxima and average results; ensure the grating is mounted perpendicular to the beam.
• Safety: never look directly into the laser beam or its reflections.

• Known: grating line density (to obtain d) and order n. Measure grating-to-screen distance L and the separation between matching −n and +n maxima.
• Calculate x as half that separation, then θ = tan⁻¹(x/L), and finally λ = d sin θ / n. No independent variable must be swept to determine λ.
• Repeat with several order pairs where visible, calculate λ for each and average. Keep laser, grating normal and central maximum aligned; never view the direct or reflected beam.

Quick-Check Questions

Short retrieval questions covering the essential ideas in Wave Nature of Light.

1. List the regions of the electromagnetic spectrum in order of increasing frequency.

2. Why does the fact that light can be polarised show that it is a transverse wave?

3. Write the diffraction grating equation and state the meaning of each symbol.

4. Why does a prism split white light into different colours?

5. Define irradiance and give its unit.

Common mistakes and exam tips

Common misconceptions and exam-technique checks for Wave Nature of Light.

• Avoid: Treating lines per millimetre as the grating spacing d. Correct idea: Convert the line density N to lines per metre, then use d = 1/N.
• Avoid: Thinking longitudinal waves can be polarised. Correct idea: Only transverse waves can be polarised; polarisation is evidence that light is transverse.
• Avoid: Confusing diffraction with dispersion. Correct idea: Diffraction is wave spreading at an aperture or obstacle; dispersion is wavelength-dependent separation.
• Avoid: Ranking radiation hazard from frequency alone. Correct idea: Hazard depends on whether radiation is ionising and on penetration, irradiance or intensity, absorbed dose, exposure time and biological effect.
• Avoid: Saying the word “intensity” is automatically wrong when irradiance is intended. Correct idea: Use the quantity defined in the question. Irradiance is radiant power per unit area in W m⁻²; “intensity” has context-dependent definitions and units.

• For a grating calculation, convert lines/mm to d in metres before using nλ = d sin θ.
• For polarisation, link the observation with crossed filters to the conclusion that light is transverse.
• For irradiance, use power in watts and area in square metres.

Exam-style questions

Five exam-style questions with worked answers on Wave Nature of Light.

Higher Level — Required Content

Required Higher Level content for this topic.

Coherent light from two slits overlaps to form alternating bright and dark fringes by constructive and destructive interference.

• n is the order, λ is wavelength, d is slit spacing and θ is measured from the central maximum.
• Measure corresponding maxima on both sides and average the angle to reduce alignment error.
• Use d = 1/N when the grating has N lines per metre.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for Wave Nature of Light.

• nλ = d sin θ (diffraction grating)
• c = fλ
• I = P/A (irradiance)

• Electromagnetic spectrum
• Diffraction grating
• Polarisation
• Dispersion
• Irradiance

• The electromagnetic spectrum in order, with wavelength/frequency trend
• Diffraction grating pattern (central and higher-order maxima)
• Dispersion of white light through a prism

• Measuring the wavelength of laser light using a diffraction grating

• Forgetting to convert lines-per-mm to slit spacing d
• Thinking longitudinal waves can be polarised
• Confusing dispersion with diffraction
• Assuming all EM waves are equally hazardous

1. A solar panel of area 2 m² receives 1000 W of solar power. Calculate the irradiance.

2. Explain why gamma rays are more hazardous to living tissue than radio waves.

3. A diffraction grating has 600 lines per mm. Calculate the slit spacing d in metres.

4. Explain how polarising sunglasses reduce glare from a reflective surface such as water.

1. I = P/A = 1000 ÷ 2 = 500 W m⁻².

2. Gamma rays have a much higher frequency (and therefore higher photon energy, E = hf) than radio waves, making them ionising and capable of damaging biological molecules such as DNA, whereas radio waves carry far too little energy per photon to ionise atoms.

3. d = 1/600 mm = 1.67 × 10⁻³ mm = 1.67 × 10⁻⁶ m.

4. Light reflected off a horizontal surface such as water becomes partially polarised in the horizontal plane; polarising sunglasses are oriented to block light polarised in that plane, reducing the glare while still allowing other (non-reflected) light through.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.

Note: irradiance (I = P/A) is confirmed in the new Leaving Certificate Physics specification's own equation list (Strand 2.4), though it does not appear as a distinct formula in the old Tables book under this name.