Huygens’ Principle is based on the following assumptions:

Each point on the primary wavefront acts as a source of secondary wavelets, sending out disturbance in all directions in a similar manner as the original source of light does.

The new position of the wavefront at any instant (called secondary wave front) is the envelope of the secondary wavelets at that instant.
Laws of Reflection on Wave Theory

Consider any point Q on the incident wavefront PA.

When the disturbance from P on incident wavefront reaches point , the disturbance from point Q reaches .

If c is velocity of light, then time taken by light to go from point Q to (via point K) is given by,

In rightangled ΔAQK,
∠QAK = i
∴ QK = AK sin i

In rightangled ,
Substituting these values in equation (1),
The rays from different points on incident wavefront will take the same time to reach the corresponding points on the reflected wavefront, if ‘t’ given by equation (ii) is independent of AK.
∴ AK (sin i − sin r) = 0
sin i − sin r = 0
sin i = sin r
i = r
i.e., the angle of incidence is equal to the angle of refraction.
Also, the incident ray (LA or), reflected ray (or ), and the normal (AN) − all lie in the same plane.
Refraction On The Basis Of Wave Theory

Consider any point Q on the incident wavefront.

Suppose when disturbance from point P on incident wavefront reaches point on the refracted wavefront, the disturbance from point Q reaches on the refracting surface XY.

Since represents the refracted wavefront, the time taken by light to travel from a point on incident wavefront to the corresponding point on refracted wavefront should always be the same. Now, time taken by light to go from Q to will be

In rightangled ΔAQK, ∠QAK = i
∴ QK = AK sin i … (ii)

In rightangled
… (iii)

Substituting (ii) and (iii) in equation (i),

The rays from different points on the incident wavefront will take the same time to reach the corresponding points on the refracted wavefront i.e., t given by equation (iv) is independent of AK. It will happen so, if
This is the Snell’s law for refraction of light.
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