Electromagnetic Waves — AP Physics 2
1. Fundamental Nature of Electromagnetic Waves ★★☆☆☆ ⏱ 2 min
Electromagnetic (EM) waves are transverse waves produced by the acceleration of charged particles, consisting of coupled oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. Unlike mechanical waves, EM waves can travel through vacuum as well as material media. This topic accounts for ~3-4% of your total AP Physics 2 exam score, appearing in both multiple-choice and free-response sections.
2. Speed, Wavelength Relations and the EM Spectrum ★★☆☆☆ ⏱ 5 min
All EM waves in vacuum travel at the constant speed $c = 3.00 \times 10^8 \text{ m/s}$, regardless of their frequency or wavelength. For any wave, the fundamental relation between speed, frequency, and wavelength holds:
c = f \lambda
When traveling through a medium with refractive index $n$, the speed becomes $v = c/n$. Frequency is determined by the source and stays constant, so wavelength scales as $\lambda_n = \lambda_0 /n$, where $\lambda_0$ is the vacuum wavelength. The full range of EM waves is the electromagnetic spectrum, ordered from lowest frequency (longest wavelength) to highest frequency (shortest wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Visible light spans only ~400 nm (violet) to 700 nm (red).
Exam tip: When an EM wave moves from one medium to another, frequency is set by the source and never changes — only speed and wavelength change. This is one of the most commonly tested conceptual points on AP multiple choice.
3. Polarization and Malus's Law ★★★☆☆ ⏱ 5 min
EM waves are transverse, meaning the electric field oscillates perpendicular to the direction of propagation. In unpolarized light, the electric field oscillates in all possible planes perpendicular to propagation. Polarized light has electric field oscillation restricted to a single plane. A polarizer only transmits the component of the electric field parallel to its transmission axis, absorbing the perpendicular component.
When unpolarized light passes through a single polarizer, intensity is always cut in half, regardless of polarizer orientation: $I_1 = I_0 / 2$. When polarized light of intensity $I_1$ is incident on a second polarizer (analyzer), the transmitted intensity follows Malus's Law:
I_2 = I_1 \cos^2 \theta
Where $\theta$ is the angle between the polarization direction of the incident light and the transmission axis of the analyzer.
Exam tip: Always remember to halve the intensity first if the incident light on the first polarizer is unpolarized. Malus's law only applies to already polarized incident light, which is a frequent AP exam error.
4. Photon Energy ★★★☆☆ ⏱ 4 min
AP Physics 2 connects EM wave properties to quantum behavior: EM radiation is quantized into discrete packets called photons, where each photon's energy depends only on the frequency (or wavelength) of the EM wave. The photon energy relation is:
E = hf = \frac{hc}{\lambda}
Where $h = 6.626 \times 10^{-34} J \cdot s$ is Planck's constant. For most AP problems involving photon energy in electron-volts (eV), the shortcut $hc \approx 1240 eV \cdot nm$ is extremely useful, as it avoids unit conversions between joules and eV when wavelength is given in nanometers. Higher frequency (shorter wavelength) EM radiation has higher energy per photon.
Exam tip: Memorize the $hc \approx 1240 eV \cdot nm$ shortcut — it saves 1-2 minutes of unit conversion on every photon energy problem on the exam.
Common Pitfalls
Why: Students memorize Malus's law and forget it only applies to incident polarized light, not unpolarized.
Why: Students confuse frequency and wavelength dependence on medium, mixing up which quantity is set by the source.
Why: Students memorize the shortcut value but forget it is only valid when wavelength is in nanometers.
Why: Students forget the inverse relationship between wavelength and energy.
Why: Students carry over properties of mechanical waves learned earlier to EM waves.