Question

How is a wavefront defined? Using Huygens’ principle draw a figure showing the propagation of a plane wave refracting at a plane surface separating two media. Hence verify Snell’s law of refraction.

Answer 1

Wavefront is the locus of all the points of the medium vibrating in the same phase.

Let XY be a plane refracting surface separating rarer medium I of refractive index µ₁, from denser medium II of refractive

index µ₂ [µ₂ > µ₁], then

\(\frac{\mu_2}{\mu_1} = 1 \mu_2 = \frac{v_1}{v_2}\)

Where v₁ is the velocity of light in medium I and v₂ is the velocity of light in medium II.

According to Huygens’ principle, every point on incident wavefront AB is a source of secondary wavelets. By the time wavelet from point B reaches at point C, the wavelet from point A would have reached at point D s.t. time taken from B to C is equal to time taken from A to D.

i.e. t = \(\frac{BC}{v_1} = \frac{AD}{v_2}\)

Let XY be a plane reflecting surface and AB be a plane wavefront incident on the surface as shown in Fig. According to Huygens’ principle, every point on wavefront AB is a source of secondary wavelets and the time during which wavelet from B reaches at C, the reflected wavelet from A would arrive at D.

If t is the time taken by wavelet from B to C [or A to D] then

Putting Eq. (ii) and (iii) in Eq. (i), we get

AC sin i = AC sin r

or sin i = sin r

or i = r

i.e. Angle of incidence = Angle of reflection.

This proves first law of reflection.