In Huygens’ construction, every point of a wavefront at time \(t = 0\) is a source of secondary wavelets. The wavelets spread out with the speed \(v\) of the wave. After a time \(\tau\), the new position of the wavefront is given by
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → the common tangent drawn to the wavelets in the forward direction
In Huygens’ construction, each point of the wavefront sends out a secondary wavelet. After time \( \tau \), each wavelet is a sphere of radius \( v\tau \).
Option (1) the surface joining the centres of the secondary wavelets — Incorrect. The centres lie on the old wavefront itself, so joining them only gives back the wavefront at \( t=0 \).
Option (2) the surface of any one secondary wavelet of radius \(v\tau\) — Incorrect. A single wavelet is only the sphere spreading from one point; the new wavefront is the surface that touches all the wavelets together.
Option (3) the common tangent drawn to the wavelets in the forward direction — Correct. The forward envelope, the common tangent to all the spheres, is the new wavefront at \( t=\tau \).
Option (4) the common tangent drawn to the wavelets in the backward direction — Incorrect. A backward envelope would be a wave travelling back towards the source; such a backwave does not exist.
NCERT (2026-27):
Huygens Principle – “Thus, if we wish to determine the shape of the wavefront at t = τ, we draw spheres of radius vτ from each point on the spherical wavefront where v represents the speed of the waves in the medium. If we now draw a common tangent to all these spheres, we obtain the new position of the wavefront at t = τ. …”
Summary – “2. Huygens’ construction tells us that the new wavefront is the forward envelope of the secondary waves. …”