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Asked in GUJCET 2024 · Wavefronts and Huygens construction
Given: two particles of the medium lying on the same wavefront.
Idea: a wavefront is defined as the surface through all the points that oscillate in the same phase -- that definition is the whole answer.
The disturbance leaves the source once and reaches every point of that surface at the same instant, so the path travelled is the same for both particles.
Path difference zero gives Δφ=(2π)/λ×0.
Δφ=0.
This is why Huygens could treat every point of a wavefront as a secondary source starting in step with all the others.
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