(a) (i) State Huygen's principle. With the help of a diagram, show how a plane wave is reflected from a surface. Hence verify the law of reflection.…

(a)

(i) Huygen's principle Each point of the wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. These wavelets emanating from the wavefront are usually referred to as secondary wavelets, a common tangent to all these spheres gives the new position of the wavefront at a later time. Verification of law of reflection In \(\displaystyle \triangle \mathrm{AEC}\) & \(\displaystyle \triangle \mathrm{CBA}\) \[\mathrm{EC}=\mathrm{AB} \quad(\mathrm{c} \times \mathrm{t} \text { each }) \] \[\angle \mathrm{AEC}=\angle \mathrm{CBA} \quad\left(90^{0} \text { each }\right) \] By RHS congruency \(\displaystyle \Delta \mathrm{AEC} \cong \Delta \mathrm{CBA}\) \[\Rightarrow \angle i=\angle r \]

(ii) \(\displaystyle m=+3, \mathrm{f}=-12 \mathrm{~cm}, u=\) ? \[m=-\frac{v}{u}=3 \Rightarrow v=-3 u \] using mirror formula \[\frac{1}{v}+\frac{1}{u}=\frac{1}{\mathrm{f}} \] \[\frac{1}{-3 u}+\frac{1}{u}=\frac{1}{-12} \] \[u=-8 \mathrm{~cm} \]