Physics: Light and Waves

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Light and Waves unifies the behaviour of electromagnetic radiation and mechanical oscillations. The single most-tested identity is the wave equation: v = fλ, where v is wave speed in m/s, f is frequency in Hz, and λ is wavelength in metres. Refraction obeys Snell’s law (n₁ sin θ₁ = n₂ sin θ₂), and beyond the critical angle (sin θ꜀ = 1/n) light undergoes total internal reflection. Interference in Young’s double-slit is constructive when path difference = nλ and destructive when it equals (n + ½)λ.

HAT-UG tests Snell’s law, critical angle, and Young’s fringe spacing as MCQs.
Remember v = fλ applies to both light and sound; only the value of v changes.
Doppler effect sign depends on direction of motion — toward = higher f, away = lower f.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Wave Fundamentals

A wave transports energy without transporting matter. Transverse waves (light, waves on a string) oscillate perpendicular to propagation; longitudinal waves (sound) oscillate parallel. The period T (s) is the reciprocal of frequency: T = 1/f. The phase of a wave determines where it lies in its cycle and is critical when comparing two sources for interference.

Reflection and Refraction

The laws of reflection — angle of incidence equals angle of reflection, with both measured from the normal — hold for plane and spherical mirrors. For refraction, Snell’s law (n₁ sin θ₁ = n₂ sin θ₂) governs bending across an interface, where the refractive index n = c/v. The apparent depth of a coin in water equals real depth divided by n.

Interference, Diffraction, Polarization

Young’s double-slit produces a fringe pattern with spacing β = λD/d, where D is slit-to-screen distance and d is slit separation. Huygens’ principle treats each point on a wavefront as a secondary source, explaining diffraction. Polarization filters transverse vibrations via Malus’s law: I = I₀ cos²θ.

Phenomenon	Key condition or formula	Medium requirement
Refraction	n₁ sin θ₁ = n₂ sin θ₂	Any transparent medium
Total internal reflection	sin θ꜀ = 1/n (denser → rarer)	Requires n₂ < n₁
Constructive interference	Path difference = nλ	Coherent sources
Destructive interference	Path difference = (n + ½)λ	Coherent sources
Polarization	Only transverse waves	Vacuum or medium

Exam Pointers for HAT-UG

Watch sign conventions in Snell’s law — match n with the side of the interface.
One HAT-UG item per paper often links wave speed, frequency, and wavelength numerically; substitute directly into v = fλ.
Decibel problems use L = 10 log₁₀(I/I₀); a 10 dB rise means 10× intensity.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Sound, Standing Waves, and the Doppler Effect

Sound travels at roughly 343 m/s in air at 20 °C, scaling with √T (Kelvin). Standing waves on a string fixed at both ends support harmonics at fₙ = nv/2L; an open pipe supports all harmonics, while a pipe closed at one end supports only odd ones. The Doppler effect for sound is f’ = f(v ± v₀)/(v ∓ vₛ); the top signs apply when observer moves toward the source or source moves toward the observer. For light, the relativistic formula replaces v with c, and the medium plays no role.

Wave-Particle Duality and the EM Spectrum

Light behaves as a wave (interference, diffraction) and as a particle (photons in the photoelectric effect, E = hf). The electromagnetic spectrum orders radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma radiation by increasing frequency and photon energy. HAT-UG questions frequently ask which band a given wavelength belongs to, or which carries the highest energy per photon.

Worked Micro-Example

Light of wavelength 600 nm enters glass of n = 1.5 at 30° incidence.

Step 1: apply Snell’s law — sin 30° = 1.5 · sin θ₂ → sin θ₂ = 0.333 → θ₂ ≈ 19.5°.
Step 2: speed in glass — v = c/n = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s.
Step 3: frequency unchanged, wavelength shrinks — λ_medium = λ₀/n = 400 nm.

Quantity	In vacuum (n = 1)	In glass (n = 1.5)
Speed v	3 × 10⁸ m/s	2 × 10⁸ m/s
Wavelength λ	600 nm	400 nm
Frequency f	5 × 10¹⁴ Hz	5 × 10¹⁴ Hz

Common Traps and Strategy

Mixing Snell’s law orientation — always keep n paired with sin θ on the same side.
Treating decibels as linear — a 20 dB gain is a 100-fold intensity jump.
Applying polarization to sound, which is longitudinal and cannot be polarized.
HAT-UG weightage: Light and Waves sits inside Subject Knowledge (≈3% of the paper). Allocate practice to numerical MCQs (Snell, v = fλ, fringe spacing) rather than derivations.

Practice Prompts

A 256 Hz tuning fork and a 260 Hz fork sound together — what is the beat frequency, and after how many seconds does the loudness cycle return to maximum?
Light in a fibre (n = 1.45) strikes the core-cladding boundary at 80° — does total internal reflection occur? Show the calculation.

Continue your study

View this topic in your HAT-UG (HEC Aptitude Test - Undergraduate) roadmap — see where “Physics: Light and Waves” fits in your personalised plan
Build a quick revision plan — 1-day sprint covering highest-weight topics
HAT-UG (HEC Aptitude Test - Undergraduate) exam overview — pattern, eligibility, and syllabus
All Subject Knowledge notes — browse sibling topics in this subject

Content adapted based on your selected roadmap duration. Switch tiers using the selector above.

Physics: Light and Waves