(a) A plane wavefront $\mathrm{AC}$ is incident on the plane of separation XY of two media of refractive indices ${\mathit{\mu }}_1$ and ${\mathit{\mu }}_2\left({\mathit{\mu }}_2>{\mathit{\mu }}_1\right)$ making an angle $\mathit{i}$. This is known as angle of incidence.
When the wavefront touches the point $\mathit{A}$, the point becomes a source of secondary wavelets. Thus, when the whole waveform passes through the $\mathit{X}\mathit{Y}$ plane, each point of AF becomes the source of secondary wavelets.

When point $\mathit{C}$ of the wavefront in medium 1 traverses CF distance by that time $\left(\mathit{t}\right)$ the wavelet from point $\mathit{A}$ traverses $\mathrm{AD}$ distance. If ${\mathit{v}}_1$ and ${\mathit{v}}_2$ are the speeds of light in medium 1 and 2 respectively, then $\mathit{A}\mathit{D}={\mathit{v}}_2\mathit{t}$ and $\mathit{C}\mathit{F}={\mathit{v}}_1\mathit{t}$.
Refracted wavefront DF which is obtained by drawing a tangent to the arc having radius ${\mathit{v}}_2\mathit{t}$ and centre $\mathrm{A}$. The angle made by the tangent with the plane $\mathrm{XY}$ is $\mathit{r}$. This is known as angle of refraction.
The perpendiculars drawn on wavefront $\mathrm{AC}$ are the incident rays. The perpendiculars drawn on wavefront $\mathit{D}\mathit{F}$ are the refracted rays.
$\mathrm{AN}$ and TF are the perpendiculars drawn on $\mathrm{XY}$, the plane of separation of the two media.
$\angle \mathit{C}\mathit{A}\mathit{F}=\angle \mathit{i}={90}^{\circ }-\angle \mathit{N}\mathit{A}\mathit{C}$ $={90}^{\circ }-\left({90}^{\circ }-\angle \mathit{S}\mathit{A}\mathit{N}\right)$
$\therefore \angle \mathit{S}\mathit{A}\mathit{N}=\angle \mathit{i}$


$\mathit{s}\mathit{i}\mathit{n}\mathit{i}=\frac{\mathit{C}\mathit{F}}{\mathit{A}\mathit{F}}=\frac{{\mathit{v}}_1\mathit{t}}{\mathit{A}\mathit{F}}$
In $△\mathrm{ADF}$,
$\mathit{s}\mathit{i}\mathit{n}\mathit{r}=\frac{\mathit{A}\mathit{D}}{\mathit{A}\mathit{F}}=\frac{{\mathit{v}}_2\mathit{t}}{\mathit{A}\mathit{F}}$
$\therefore \frac{\mathit{s}\mathit{i}\mathit{n}\mathit{i}}{\mathit{s}\mathit{i}\mathit{n}\mathit{r}}=\frac{{\mathit{c}}_1\mathit{t}}{{\mathit{c}}_2\mathit{t}}=\frac{{\mathit{c}}_1}{{\mathit{c}}_2}={}_1{\mathit{\mu }}_2$
This is Snell's law.
OR
(b) A plane wavefront $\mathrm{AC}$ is incident on a plane reflector $\mathrm{XY}$ making an angle $\mathit{i}$. This is known as angle of incidence.
Each and every point of the wavefront when touches the reflector becomes a source of secondary wavelets. When the wavefront touches the point $\mathrm{A}$, the point becomes a source of secondary wavelets. Thus, when the whole waveform touches the XY plane, each point of AF becomes the source of secondary wavelets. When point $\mathrm{C}$ of the wavefront in medium 1 traverses CF distance by that time $\left(\mathit{t}\right)$ the wavelet from point $\mathrm{A}$ traverses $\mathrm{AD}$ distance. If ${\mathit{v}}_1$ is the speeds of light in medium then $\mathit{A}\mathit{D}={\mathit{v}}_1\mathit{t}$ and $\mathit{C}\mathit{F}={\mathit{v}}_1\mathit{t}$.
Reflected wavefront DF which is obtained by drawing a tangent to the arc having radius ${\mathit{v}}_1\mathit{t}$ and centre $\mathrm{A}$. The angle made by the tangent with the plane $\mathrm{XY}$ is $\mathit{r}$. This is known as angle of refraction.

The perpendiculars drawn on wavefront $\mathit{A}\mathit{C}$ are the incident rays. The perpendiculars drawn on wavefront DF are the reflected rays.
$\mathrm{AN}$ and TF are the perpendiculars drawn on $\mathrm{XY}$, the plane reflector.
$\angle \mathit{C}\mathit{A}\mathit{F}=\angle \mathit{i}={90}^{\circ }-\angle \mathit{N}\mathit{A}\mathit{C}$
$={90}^{\circ }-\left({90}^{\circ }-\angle \mathit{S}\mathit{A}\mathit{N}\right)$
$\therefore \angle \mathit{S}\mathit{A}\mathit{N}=\angle \mathit{i}$

In $△\mathrm{ACF}$ and $△\mathrm{AFD}$
$\angle \mathit{A}\mathit{C}\mathit{F}=\angle \mathit{A}\mathit{D}\mathit{F}={90}^{\circ }$
$\mathit{C}\mathit{F}=\mathit{A}\mathit{D}$
$\mathrm{AF}$ is the common side
So, the triangles are congruent.
$\therefore \angle \mathit{C}\mathit{A}\mathit{F}=\angle \mathit{A}\mathit{F}\mathit{D}$
$\therefore \mathit{i}=\angle \mathit{r}$
This is law of reflection.