(a) A plane wavefront AC is incident on the plane of separation XY of two media of refractive indices µ1 and µ2(µ2>µ1) making an angle i. This is known as angle of incidence.
When the wavefront touches the point A, the point becomes a source of secondary wavelets. Thus, when the whole waveform passes through the XY plane, each point of AF becomes the source of secondary wavelets.

When point C of the wavefront in medium 1 traverses CF distance by that time (t) the wavelet from point A traverses AD distance. If v1 and v2 are the speeds of light in medium 1 and 2 respectively, then AD=v2t and CF=v1t.
Refracted wavefront DF which is obtained by drawing a tangent to the arc having radius v2t and centre A. The angle made by the tangent with the plane XY is r. This is known as angle of refraction.
The perpendiculars drawn on wavefront AC are the incident rays. The perpendiculars drawn on wavefront DF are the refracted rays.
AN and TF are the perpendiculars drawn on XY, the plane of separation of the two media.
∠CAF=∠i=90∘−∠NAC =90∘−(90∘−∠SAN)
∴‌∠SAN=∠i
‌ Similarly, ‌‌∠QFT=∠r
‌ In ‌△ACF,‌
‌sin‌i=‌

CF

AF

=‌

v1t

AF

In △ADF,
sin‌r‌=‌

AD

AF

=‌

v2t

AF

∴‌‌‌

sin‌i

sin‌r

=‌

c1t

c2t

=‌

c1

c2

=‌1µ2
This is Snell's law.
OR
(b) A plane wavefront AC is incident on a plane reflector XY making an angle 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 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 C of the wavefront in medium 1 traverses CF distance by that time (t) the wavelet from point A traverses AD distance. If v1 is the speeds of light in medium then AD=v1t and CF=v1t.
Reflected wavefront DF which is obtained by drawing a tangent to the arc having radius v1t and centre A. The angle made by the tangent with the plane XY is r. This is known as angle of refraction.

The perpendiculars drawn on wavefront AC are the incident rays. The perpendiculars drawn on wavefront DF are the reflected rays.
AN and TF are the perpendiculars drawn on XY, the plane reflector.
∠CAF‌=∠i=90∘−∠NAC
‌=90∘−(90∘−∠SAN)
∴‌‌∠SAN‌=∠i
‌ Similarly, ‌‌‌∠QFT‌=∠r
In △ACF and △AFD
∠ACF‌=∠ADF=90∘
CF‌=AD
AF is the common side
So, the triangles are congruent.
∴‌‌∠CAF‌=∠AFD
∴i‌=∠r
This is law of reflection.