Chapter 29, Problem 1RCQ

To determine

Huygens’s hypothesis of every point on a wavefront.

Answer to Problem 1RCQ

Solution:

Every point on a wavefront behaves as a secondary wavelet according to Huygens’s hypothesis.

Explanation of Solution

Huygens gave a principle through which we can imagine or geometrically construct the position of a wavefront at any instant. His hypothesis is

" Every point of wavefront behaves like a secondary wavelet which moves with the velocity of light in all directions ".
The meaning of Secondary wavelet is that every point on the wavefront behaves as a fresh source of the new disturbance. Let AB be a primary wavefront, then according to Huygens’s principle, every point on this wavefront behaves like a secondary wavelet. To determine the position of the wavefront after some time t, we take a help from geometry. The distance traveled by light in t seconds = ct. Then we make spheres of radius ct by taking every point on a primary wavefront as centers of those spheres. All those surfaces of spheres represent the position of secondary wavelets at time t. Drawing a surface A'B' touching those surfaces of spheres. It will be the position wavefront after time t.

Huygens Hypothesis

Conclusion:

We saw that Huygens imagined all point on (primary) wavefront as a secondary wavelet which also led us to know that wavefront travel parallels to itself.