Refraction of a plane wavefront at a plane surface
Let XY be a plane refracting surface separating two media 1 and 2 of refractive indices μ1 and μ2 (Figure). The velocities of light in these two media are respectively c1 and c2. Consider a plane wave front AB incident on the refracting surface at A. PA and QBC are perpendiculars drawn to AB at A and B respectively. Hence they represent incident rays. NAN1 is the normal drawn to the surface. The wave front and the surface are perpendicular to the plane of the paper.
Fig: Refraction of a plane wavefront at the plane surface.
According to Huygen’s principle each point on the wave front act as the source of secondary wavelet. By the time, the secondary wavelets from B, reaches C, the secondary wavelets from the point A would travel a distance AD = C2t, where t is the time taken by the wavelets to travel the distance BC.
∴ BC = C1t and AD = C2t = C2 BC/C1.
Taking A as centre and C2 BC/C1 as radius an arc is drawn in the second medium. 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 refracted plane wavefront and AD is the refracted ray.