Classify interference using path difference and combine signed wave amplitudes.
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Method and worked examples
Superposition means that overlapping wave fields add at each point. Equal in-phase amplitudes reinforce, while equal amplitudes separated by half a cycle cancel. In-phase sources give constructive interference when path difference is mλ and destructive interference when it is (m+ ½)λ, where m is an integer. A field cancellation at one point does not mean energy disappears; the intensity pattern redistributes it.
Monochromatic light has one frequency. Coherent sources maintain a fixed phase relationship, which is needed for a stationary interference pattern. Equal frequency alone does not guarantee a stable phase relationship between independent lamps. At a given instant, add signed displacements or electric-field components algebraically. If the field amplitudes double coherently, intensity becomes four times as large because intensity is proportional to amplitude squared.
Example 1
Two in-phase sources emit wavelength 600 nm. Classify a point with path difference 900 nm.
600900=1.50 wavelengths, so the waves arrive half a cycle out of phase and destructively interfere.
Example 2
Two equal fields each have amplitude A. Compare intensity for in-phase overlap with one field alone.
The resultant amplitude is 2A; intensity ∝ A2, so the intensity is four times that of one field.
Watch out:They must also maintain a constant phase relationship to produce a stable interference pattern.
Coherence, phase and superposition practice | Year 12 Physics | Ascent Arcade