**Reflection of a plane wave front at a plane surface**

Let XY be a plane reflecting surface and AB be a plane wavefront incident on the surface at A. PA and QBC are perpendiculars drawn to AB at A and B respectively. Hence they represent incident rays. AN is the normal drawn to the surface. The wave front and the surface are perpendicular to the plane of the paper (Figure).

Fig: Reflection of a plane wavefront at a plane surface.

According to Huygen’s principle each point on the wavefront acts as the source of secondary wavelet. By the time, the secondary wavelets from B travel a distance BC, the secondary wavelets from A on the reflecting surface would travel the same distance BC after reflection.

Taking A as centre and BC as radius an arc is drawn. From C a tangent CD is drawn to this arc. This tangent CD not only envelopes the wavelets from C and A but also the wavelets from all the points between C and A. Therefore CD is the reflected plane wavefront and AD is the reflected ray.

**Laws of reflection**

(i) The incident wavefront AB, the reflected wavefront CD and the reflecting surface XY all lie in the same plane.

(ii) Angle of incidence i = ∠ PAN = 90^{0} − ∠ NAB = ∠BAC

Angle of reflection r = ∠ NAD = 90^{0} − ∠ DAC = ∠DCA

In right angled triangles ABC and ADC

∠B = ∠ D = 90^{0}

BC = AD and AC is common

∴ The two triangles are congruent

∠ BAC = ∠DCA

i.e. i = r

Thus the angle of incidence is equal to angle of reflection.