Question

Explain huygen,s principal of secondary wavelets and on the basis of this principle establish the law of Refraction ,or, reflection

Answer 1

Huygens ’ Principle enables us to determine what its position will be at some later time. In other words, the principle gives a method to know as to how light spread out in the medium. A source of light sends out wave front is propagated forwards through a homogeneous isotropic medium, Christian Huygens made the following assumptions.

Each point on a wave front acts as a new source of the disturbance. The disturbances from these points are secondary wave lets. These wavelets spread out in all directions in the medium with the velocity of light.

The new wave front is then obtained by constructing a tangential plane to all the secondary wavelets. The new wave front is the envelope of to secondary wavelets at that instant.

Answer 2

Answer: This principle is also called the Huygens-Fresnel Principle.

Explanation: Huygens’ Principle states that every point on a wavefront is the source of wavelets that spread out in the forward direction at the same speed as the wave itself.

It further elaborates on the movement of these wavelets, highlighting that they spread in all directions exactly like the primary source wave. It also mentions how at any instant of time, a tangent on any of the wavelets can give rise to a new wavefront.

The important considerations of Huygens’ Principle are:

1. All the rays, i.e., the tangents, are always perpendicular to the primary wavefront.
2. The time taken by a wave to travel from one wavefront to another will always remain constant. For a differing medium, the density may cause a change in velocity and distance, but time will remain the same.
3. All the points on a particular wavefront act like another source of spherical waves called secondary wavelets.
4. The velocity of light is changed when the light wave passes from one medium to another. This phenomenon of the bending of light is called the refraction of light.
5. Since Huygens’ Principle states that despite differences in density, the time taken by the waves to travel will be the same, let’s assume the time taken is t.

In the diagram attached below:

sini/sinr = BC/AC ÷ AD/AC

             = BC/AD

             = V1t/V2t

             = V1/V2

             = u

Here, u is a constant. It represents the refractive index of the medium through which the light rays are travelling. Another keen observation is that the incident and refracted wavefront lie on the same plane as the normal. This proves the 2nd law of refraction.

The refractive index is also calculated as the ratio of the velocity of light in a vacuum or air to the velocity of light in another medium.

Hence, Snell’s law of refraction is proved via the application of Huygens’ Principle. This proves the first law of refraction.

Conclusion:

Huygens’ Principle analyses the movement of waves across dimensions and helps us understand the unpredictability of their behaviour. Consequently, this principle is used to prove the laws of reflection and refraction of light, which are two of the most important phenomena demonstrated by light waves and attest to their behaviour as electromagnetic waves.

The approach to proving these laws using Huygens’ Principle focuses on proving the angular observations of incident and reflected or refracted rays. The consideration of Huygens’ principle that the time taken by the light waves to travel through different media, even though it remains the same, also contributes to this analysis.

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