Wavefronts and interference of light

Physics · Physical optics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A wavefront is a surface on which all points are in the same phase of vibration. A point source gives spherical wavefronts; far from the source a small part is nearly plane. Rays are at right angles to wavefronts. Huygen's principle says every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the surface that touches (is tangent to) these wavelets.

Steady interference needs coherent sources: sources with a constant phase difference, giving light of a single wavelength. Young got them by letting one source light two narrow slits. Bright fringes appear where the path difference is a whole number of wavelengths, dark fringes where it is an odd number of half wavelengths.

Rules to remember

Common mistake

Mixing units in Δy = λL/d. Change nm and mm to metres first (1 nm = 10−9 m, 1 mm = 10−3 m), and remember d is the slit separation, not the slit width.

Worked example

In Young's experiment light of wavelength 500 nm passes through slits 0.25 mm apart. The screen is 1.5 m away. Find the fringe spacing.

  1. λ = 500 × 10−9 m = 5.0 × 10−7 m and d = 0.25 mm = 2.5 × 10−4 m.
  2. Δy = λL/d = (5.0 × 10−7 × 1.5) ÷ (2.5 × 10−4).
  3. Δy = (7.5 × 10−7) ÷ (2.5 × 10−4) = 3.0 × 10−3 m.

Answer: Fringe spacing = 3.0 mm.

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