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Oblique wavefronts → effective separation Δx

Two points along a boundary hit by wavefronts at angle θ: effective separation is Δx = d sin θ (perpendicular distance between wavefronts through the points), THEN Δφ = (Δx/λ)2π. Draw the right triangle — the setup mark is the hard mark (N95 sea-wall).

What this actually means

When wavefronts arrive at an angle to a line of points, the separation that matters is not the distance d between the points but its component along the travel direction: Δx = d sin θ.

Draw the right-angled triangle between a wavefront and the line of points; that setup is where the hard mark sits. Then feed Δx into (Δx/λ) × 2π exactly as usual.

The N95 sea-wall question is this card in exam clothing: two posts on a wall, waves arriving obliquely, one triangle to draw.

Prove it — watch it be true

  1. Switch to oblique incidence and place two points distance d apart
  2. Watch the Δx = d·sinθ triangle build itself between the wavefronts
  3. Vary θ: at 90° the full d counts; at 0° the points are hit together
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