Patterns that move through everything.

Waves & Optics

From ripples on a pond to laser light, waves carry energy without carrying matter. Optics studies how light reflects, refracts, and interferes.

Signaturev = f·λ

Chapter outline

Lessons in this chapter

Short, focused lessons. Each one ends with a worked example and a quick quiz.

Key concepts at a glance

The essential ideas, paired with their equations.

Wave Equation

01
v = f·λ

Wave speed equals frequency times wavelength.

Snell's Law

02
n₁ sinθ₁ = n₂ sinθ₂

How light bends when crossing materials of different optical density.

Doppler Effect

03
f' = f·(v±vₒ)/(v∓vₛ)

Why a passing siren shifts pitch — motion compresses or stretches waves.

Interference

04

Overlapping waves add — sometimes amplifying, sometimes cancelling.

Diffraction

05

Waves bend around obstacles and through slits, revealing their wave nature.

Polarization

06

Restricting the plane in which a transverse wave oscillates.

Frequently asked

What is the difference between transverse and longitudinal waves?+

Transverse waves oscillate perpendicular to their motion (light); longitudinal waves oscillate along it (sound).

Why does light bend in water?+

Light slows down in denser media, refracting toward the normal — described by Snell's law.

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