Explain the reflection of plane waves using Huygens' principle. OR Explain single slit diffraction. On what factors does the width of the central maximum depend?

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> [!TLDR]
> Using Huygens' secondary wavelet construction on a plane wavefront striking a reflecting surface, simple geometry (congruent triangles) proves the angle of reflection equals the angle of incidence.
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> Consider a plane wavefront $AB$ incident on a plane reflecting surface $MN$ at angle of incidence $i$, such that point $A$ touches the surface first while $B$ is still travelling towards it. Let $v$ be the speed of the wave and $	au$ the time taken for the disturbance from $B$ to reach the surface at point $C$; in this time, $BC = v	au$.
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> According to Huygens' principle, while the disturbance from B travels to C, the point A (already on the surface) acts as a source of secondary wavelets, which spread out into the same medium (since it's reflection) and travel the same distance $v	au$ in time $	au$. So, with A as centre, draw an arc of radius $AD = v	au$; the tangent plane $CD$ drawn from $C$ to this arc gives the new (reflected) wavefront.
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> Now, in right triangles $ABC$ and $ADC$: $BC = AD = v	au$ (both equal to the same distance travelled in time $	au$), and $AC$ is common to both triangles, with both having a right angle (since $BC \perp$ direction of incident wave at $C$, and $AD \perp$ direction of reflected wave at $A$, in the standard construction). Hence the triangles are congruent (RHS congruence), so the angle $\angle BAC$ (angle of incidence, $i$) equals the angle $\angle DCA$ (angle of reflection, $r$):
> $$i = r$$
> This is the law of reflection, derived using Huygens' principle. Also, the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
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Q.Explain the reflection of plane waves using Huygens' principle.

Concept understanding — Reflection of Light Using Huygens' Principle

Q.Explain the reflection of plane waves using Huygens' principle.

Concept understanding — Reflection of Light Using Huygens' Principle

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