Explain the reflection of a plane wave using Huygen's principle.
Explain the reflection of a plane wave using Huygen's principle.
Consider a plane wave $\mathrm{AB}$ incident at an angle $i$ on a reflecting surface $\mathrm{MN}$.
The velocity of wave in medium is $v$ and $\tau$ is time to move the wavefront from point $\mathrm{B}$ to $\mathrm{C}$. $\therefore \mathrm{BC}=v \tau$
As shown in figure plane wave $\mathrm{AB}$ is incident on reflective surface $\mathrm{MN}$ and its reflective wavefront
is $\mathrm{CE}$.
In figure $\triangle \mathrm{EAC}$ and $\triangle \mathrm{BAC}$ are similar triangles,
Here, $\mathrm{AE}=\mathrm{BC}=v \tau$
$\angle \mathrm{AEC}=\angle \mathrm{ABC}$
and $\mathrm{AC}=\mathrm{AC}$
hence $\angle \mathrm{BAC}=\angle \mathrm{ECA}$
$\therefore i=r$ is the law of reflection.
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