C.3 Wave phenomena

UNIT SYLLABUS

SL/HL 5 hours SL + 6 hours HL

This is where waves do things particles never could. At boundaries they reflect and refract (Snell's law, total internal reflection — the physics of optical fibres); around obstacles they diffract; and when two coherent waves meet they interfere, adding crest-on-crest or cancelling crest-on-trough. Young's double-slit experiment turns that superposition into a measuring instrument fine enough to determine the wavelength of light with a ruler. HL sharpens the picture with single-slit diffraction — whose envelope modulates the double-slit pattern — and diffraction gratings, which power every spectrometer that has ever decoded starlight.

Guiding Questions

? How do waves behave at boundaries between different media?
? What happens when two waves occupy the same region of space at the same time?

✓ What the IB expects you to master

Describe two- and three-dimensional waves using wavefronts and rays.
Analyse reflection, refraction and transmission at boundaries, including wavefront–ray diagrams.
Apply Snell's law $\frac{n_1}{n_2} = \frac{\sin\theta_2}{\sin\theta_1} = \frac{v_2}{v_1}$ , the critical angle, and total internal reflection.
Describe diffraction around bodies and through apertures, and its dependence on the ratio $\lambda/b$ .
Explain superposition of waves and pulses, and the need for coherent sources in double-source interference.
Use the interference conditions: constructive at path difference $n\lambda$ , destructive at $(n+\frac{1}{2})\lambda$ .
Apply Young's double-slit equation $s = \frac{\lambda D}{d}$ for fringe spacing.
HL: use single-slit diffraction ( $\theta = \lambda/b$ for the first minimum) and explain how it modulates the double-slit pattern.
HL: analyse multiple slits and diffraction gratings with $n\lambda = d\sin\theta$ .

1 Key Formulas

Snell's law

\frac{n_{1}}{n_{2}} = \frac{\sin\theta_{2}}{\sin\theta_{1}} = \frac{v_{2}}{v_{1}}

Refractive index

n = \frac{c}{v}

Constructive interference

\text{path difference} = n\lambda

Destructive interference

\text{path difference} = \left(n + \tfrac{1}{2}\right)\lambda

Double-slit fringe spacing

s = \frac{\lambda D}{d}

Single-slit first minimum (HL)

\theta = \frac{\lambda}{b}

Diffraction grating maxima (HL)

n\lambda = d\sin\theta

2 Exam Preparation & Topic Explanations

Interference calculations that always land

Every interference question reduces to path difference. Constructive: whole wavelengths. Destructive: odd half-wavelengths. State that first, then substitute the geometry — double slit, grating, or thin film.

For gratings, remember maxima are sharp and bright (many slits reinforce), and always check $n\lambda \le d$ to count visible orders.

Pro Exam Strategy

Snell's law in the IB data booklet form has the indices inverted relative to many textbooks: $n_1\sin\theta_1 = n_2\sin\theta_2$ is safest to work from.
Angles are measured from the NORMAL, never the surface.
Grating question: convert "lines per mm" to slit spacing $d$ in metres first, before anything else.
HL: missing orders occur when a double-slit maximum coincides with a single-slit minimum — the envelope kills it.

3 MCQ Practice

Q1. Light travels from glass ( $n = 1.5$ ) towards air. The critical angle is approximately:

30°
42°
48°
60°

Q2. In a double-slit experiment, the slit separation is doubled and the screen distance halved. The fringe spacing becomes:

Four times larger
Unchanged
A quarter of the original
Half the original

Q3. Sound diffracts around a doorway much more than light does because:

Sound travels more slowly than light
Sound is longitudinal and light is transverse
Sound's wavelength is comparable to the width of the doorway
Sound has more energy than light

4 Short Answer Questions

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