05Light and Electromagnetic Waves
Map the electromagnetic spectrum, apply Snell's law and the thin-lens equation, analyse double-slit interference, and discover the quantum photoelectric effect.
Light is the primary way we observe the universe. Understanding electromagnetic waves connects classical optics to modern quantum physics — from fibre-optic internet to medical imaging and solar cells.
How does light travel, bend, and interact with matter — and why does it sometimes behave like a wave and sometimes like a particle?
Lesson Overview
Light is an electromagnetic wave — a self-propagating oscillation of electric and magnetic fields that requires no medium. All electromagnetic waves travel at the same speed in a vacuum (c = 3 × 10⁸ m/s), but differ in frequency and wavelength across the electromagnetic spectrum. In this lesson you will map the spectrum from radio waves to gamma rays, apply Snell's law to trace refracted rays, use the thin-lens equation to locate images, analyze double-slit interference patterns, and explore the photoelectric effect — the quantum evidence that light also behaves as discrete packets of energy called photons.
The Electromagnetic Spectrum
Frequency increases (and wavelength decreases) from radio → gamma. All regions travel at c in a vacuum.
Key Equations
Worked Examples
A ray of light travels from water (n₁ = 1.33) into glass (n₂ = 1.50) at an angle of incidence θ₁ = 30°. Find the angle of refraction θ₂.
Write Snell's law: n₁ sin θ₁ = n₂ sin θ₂
Substitute: 1.33 × sin 30° = 1.50 × sin θ₂
1.33 × 0.500 = 1.50 × sin θ₂
0.665 = 1.50 × sin θ₂
sin θ₂ = 0.665 / 1.50 = 0.4433
θ₂ = sin⁻¹(0.4433) ≈ 26.3°
Find the critical angle for total internal reflection at a glass (n₁ = 1.50) to air (n₂ = 1.00) interface.
At the critical angle, the refracted ray travels along the boundary (θ₂ = 90°)
Snell's law becomes: n₁ sin θ_c = n₂ sin 90° = n₂
sin θ_c = n₂ / n₁ = 1.00 / 1.50 = 0.6667
θ_c = sin⁻¹(0.6667) ≈ 41.8°
A converging lens has focal length f = 20 cm. An object is placed 30 cm in front of the lens. Find the image distance d_i and the magnification m.
Thin lens equation: 1/f = 1/d_o + 1/d_i
1/d_i = 1/f − 1/d_o = 1/20 − 1/30
1/d_i = 3/60 − 2/60 = 1/60
d_i = 60 cm (positive → real image on opposite side)
m = −d_i / d_o = −60 / 30 = −2
In a double-slit experiment, the slit separation is d = 0.50 mm and the wavelength of light is λ = 600 nm. Find the angle θ for the first-order (m = 1) bright fringe.
Convert: d = 0.50 mm = 5.0 × 10⁻⁴ m; λ = 600 nm = 6.0 × 10⁻⁷ m
Condition for bright fringe: d sin θ = mλ
sin θ = mλ / d = (1 × 6.0 × 10⁻⁷) / (5.0 × 10⁻⁴)
sin θ = 1.2 × 10⁻³
θ = sin⁻¹(1.2 × 10⁻³) ≈ 0.069°
Light of frequency f = 8.0 × 10¹⁴ Hz strikes a metal surface with work function φ = 2.0 eV. Find the photon energy and the maximum kinetic energy of the ejected electrons.
Photon energy: E = hf = (6.626 × 10⁻³⁴ J·s)(8.0 × 10¹⁴ Hz)
E = 5.30 × 10⁻¹⁹ J
Convert to eV: E = 5.30 × 10⁻¹⁹ / 1.602 × 10⁻¹⁹ ≈ 3.31 eV
KE_max = hf − φ = 3.31 eV − 2.0 eV = 1.31 eV
Guided Problems
Light travels from air (n = 1.00) into water (n = 1.33) at θ₁ = 45°. Find the angle of refraction.
Hint: Apply Snell's law: sin θ₂ = (n₁/n₂) sin θ₁ = (1.00/1.33) × sin 45°. Compute sin 45° ≈ 0.7071 first.
Find the critical angle for total internal reflection at a diamond (n = 2.42) to air (n = 1.00) interface.
Hint: Use sin θ_c = n₂/n₁ = 1.00/2.42. Take the inverse sine to find θ_c.
A diverging lens has focal length f = −15 cm. An object is 25 cm from the lens. Find d_i and m.
Hint: Use 1/d_i = 1/f − 1/d_o with f = −15 cm. A negative d_i means a virtual image on the same side as the object.
In a double-slit setup with d = 0.30 mm and λ = 500 nm, find the angle for the second-order (m = 2) bright fringe.
Hint: Use d sin θ = mλ with m = 2. Convert d and λ to the same units (metres) before dividing.
A photon has energy E = 4.5 eV. Does it eject electrons from a metal with work function φ = 5.1 eV? If so, what is KE_max?
Hint: Compare E with φ. Electrons are only ejected when E > φ. KE_max = E − φ (can be negative, meaning no ejection).
Key Vocabulary
Electromagnetic Spectrum
The full range of electromagnetic radiation ordered by frequency (or wavelength), from low-frequency radio waves to high-frequency gamma rays. All regions travel at c = 3 × 10⁸ m/s in a vacuum.
Example: Visible light (400–700 nm) is a tiny slice of the full spectrum.
Index of Refraction
A dimensionless number n = c/v that describes how much slower light travels in a medium compared with a vacuum. A higher index means greater bending at an interface.
Example: n_water ≈ 1.33 means light travels at c/1.33 ≈ 2.26 × 10⁸ m/s in water.
Snell's Law
The relationship n₁ sin θ₁ = n₂ sin θ₂ that governs how a ray of light changes direction when it crosses the boundary between two media of different refractive indices.
Example: A ray entering glass from air bends toward the normal because n_glass > n_air.
Total Internal Reflection
When light in a denser medium strikes a boundary at an angle greater than the critical angle θ_c = sin⁻¹(n₂/n₁), all light is reflected back — none is transmitted.
Example: Optical fibres use total internal reflection to guide light over long distances.
Thin Lens Equation
The equation 1/f = 1/d_o + 1/d_i relating the focal length f of a thin lens to the object distance d_o and image distance d_i.
Example: f = 20 cm, d_o = 30 cm → d_i = 60 cm (real, inverted image).
Magnification
The ratio m = −d_i/d_o giving the size and orientation of an image relative to the object. |m| > 1 means magnified; m < 0 means inverted.
Example: m = −2 means the image is twice as tall as the object and inverted.
Double-Slit Interference
When coherent light passes through two narrow slits separated by distance d, the path-length difference d sin θ = mλ produces bright fringes at integer values of m.
Example: Young's double-slit experiment was the first strong evidence for the wave nature of light.
Photoelectric Effect
The emission of electrons from a metal surface when light of sufficient frequency strikes it. Explained by Einstein using photons: KE_max = hf − φ, where φ is the work function.
Example: No electrons are emitted if f < φ/h, regardless of light intensity — evidence for quantisation.
Workbook Check — Interactive Quiz
Interactive Practice — 5 Questions
Which region of the electromagnetic spectrum has the shortest wavelength?
Light travels from glass (n = 1.50) into air (n = 1.00) at θ₁ = 30°. Using Snell's law, what is sin θ₂?
A converging lens (f = 10 cm) has an object at d_o = 40 cm. What is the image distance d_i?
In a double-slit experiment (d = 4.0 × 10⁻⁴ m, λ = 500 nm), what is sin θ for the m = 1 bright fringe?
A photon has frequency f = 6.0 × 10¹⁴ Hz. What is its energy in eV? (h = 6.626 × 10⁻³⁴ J·s; 1 eV = 1.602 × 10⁻¹⁹ J)
Independent Practice
Light travels from air (n = 1.00) into glass (n = 1.50) at an angle of incidence of 40°. Find the angle of refraction using Snell's law.
A concave mirror has a focal length of 15 cm. An object is placed 45 cm in front of the mirror. Find (a) the image distance and (b) the magnification.
A converging lens has a focal length of 20 cm. An object is placed 60 cm from the lens. Find the image distance and state whether the image is real or virtual.
Calculate the critical angle for total internal reflection at a glass-air interface. (n_glass = 1.52, n_air = 1.00)
★ A double-slit experiment uses light of wavelength 550 nm. The slits are 0.30 mm apart and the screen is 2.0 m away. (a) Calculate the fringe spacing. (b) Find the position of the 3rd bright fringe from the center. (c) If the slit separation is halved, how does the fringe spacing change? (d) What would happen to the pattern if one slit were covered?
ChallengeCommon Mistakes
Thinking visible light is the only type of electromagnetic wave
The EM spectrum includes radio, microwave, infrared, visible, UV, X-ray, and gamma rays — all travel at c = 3×10⁸ m/s in vacuum
Confusing frequency and wavelength ordering in the EM spectrum
Higher frequency = shorter wavelength = more energy per photon. Gamma rays have the highest frequency; radio waves have the lowest
Using c = 3×10⁸ m/s for light speed inside a medium
Light slows down in a medium: v = c/n where n is the index of refraction. Only in vacuum does light travel at exactly c
Forgetting that the electric and magnetic fields in an EM wave are perpendicular to each other AND to the direction of propagation
EM waves are transverse: E ⊥ B ⊥ direction of travel. The wave carries energy in the direction of E × B (Poynting vector)
Math Tips
Photon energy: E = hf = hc/λ where h = 6.626×10⁻³⁴ J·s. In eV: E(eV) = 1240/λ(nm). Visible light (400–700 nm) has photon energies of about 1.8–3.1 eV
EM spectrum memory (low→high frequency): Radio, Microwave, Infrared, Visible (ROYGBIV), UV, X-ray, Gamma. 'Raging Martians Invaded Venus Using X-ray Guns'
Intensity of EM wave: I = P/A = ε₀cE²/2 (average). Intensity decreases as 1/r² from a point source: I ∝ 1/r²
Index of refraction: n = c/v. For common materials: air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42. Higher n means slower light and more bending