C.3 Wave phenomena (HL)

Wave phenomena describe how waves behave at boundaries and apertures. Refraction, interference and diffraction all arise from changes in wave speed and the superposition of coherent waves.

Key ideas

Wavefronts represent phase; rays represent energy flow.
Refraction occurs because wave speed changes between media.
Interference patterns depend on path difference.
Diffraction becomes significant when aperture size is comparable to wavelength.

Important formulas

n_1 \sin\theta_1 = n_2 \sin\theta_2

Snell’s law relating angles of incidence and refraction at a boundary.

\sin\theta_c = \dfrac{n_2}{n_1}

Expression for the critical angle when light travels from a denser to a rarer medium.

\Delta L = n\lambda

Condition for constructive interference between coherent waves.

\Delta L = \left(n+\tfrac{1}{2}\right)\lambda

Condition for destructive interference.

y = \dfrac{\lambda D}{d}

Fringe spacing in Young’s double-slit experiment for a distant screen.

a\sin\theta = \lambda

Angular position of the first diffraction minimum for a single slit.

d\sin\theta = n\lambda

General condition for principal maxima from a diffraction grating.

Practice problems

Wavefronts, rays and refraction

Describe how wavefronts and rays are represented for a plane wave entering glass from air at an angle. Use this description to state Snell’s law in words and symbols.

Critical angle and total internal reflection

Light travels inside glass of refractive index 1.50 towards a glass–air boundary. Calculate the critical angle and describe what happens for angles of incidence greater than this value.

Young’s double-slit interference

Light of wavelength 520 nm illuminates two slits separated by 0.20 mm. A screen is placed 1.8 m away. Calculate the distance between adjacent bright fringes.

Path difference and fringe type

At a point on a double-slit screen, the path difference is 1.5λ. State whether the point corresponds to a maximum or minimum intensity and explain why.

Single-slit diffraction minimum

Light of wavelength 620 nm passes through a slit of width 0.40 mm. Calculate the angular position of the first diffraction minimum and describe the effect of narrowing the slit.

Diffraction grating condition

A diffraction grating has 500 lines per millimetre and is illuminated normally with light of wavelength 550 nm. Calculate the angle of the first-order maximum.