Table of Contents

## Introduction:

**Refraction Using Huygens Principle: ****Huygens principle** planned by Christian Huygens in 1678 revolutionized our understanding of light and its characteristics. Huygens principle is one of the key ways for learning varied optical phenomena. The principle may be a technique of research applied to issues of wave propagation each within the far-field limit and in the near-field optical phenomenon and conjointly reflection. It states that:

‘Every purpose of a wavefront consists in itself of spherical wavelets that appear at the speed of light in a forward direction. The total of those spherical wavelets is the wavefront”.

However, this theory didn’t make a case for why refraction occurred in the 1st place. Secondly, it couldn’t explain how light carries energy because it travels.

Christian Huygens Principle, additionally called the Huygens–Fresnel principle highlights the subsequent wave propagation behavior:

Secondary sources form their own wavelets that are kind of like the first source.

At any given purpose in time, the common tangent on the wavelets in the forward direction offers the new wavefront.

Summaries the spherical wavelets to get the wavefront.

**Primary and Secondary Sources**

Huygens stated that light is a wave that propagates via an area just like ripples in water or sound in air. Hence, light unfolds out like a wave together in all directions from a source. The locus of factors that traveled far at some point of a hard and fast time interval is known as a wavefront. Thus, from a point source of light, the locus of points that light has traveled at some point of a fixed term is a sphere (a circle in case you recall a 2D source).

After the number one wavefront is created, a secondary wavefront is made out of each primary wavefront. Secondly, each point at the wavefront acts as a secondary supply of mild that emits extra wavefronts.

The net impact is that the powerful wavefront generated is tangential to all of the secondary wavefronts generated through the secondary sources as proven inside the figure. In this way, a light wave propagates via the area by producing secondary sources and wavefronts.

The course of the traverse is continually perpendicular to the wavefronts.

Huygens’ idea explains the wave idea of light phenomena of diffraction, interference, reflection, and refraction well, thinking about it becomes proposed centuries ago.

**Wavefront**

A wavefront is the collection of all the points in the same phase. We will discuss different types of wavefronts below.

**Spherical Wavefront**

When an energy source radiates, the particles around it start to oscillate, which creates waves that travel in all directions and form a spherical wavefront.

**Planar Wavefront**

Waves coming from the source are parallel if the source is at infinity (light rays are parallel on Earth if the sun is at infinity). A planar wavefront forms in such cases.

**Cylindrical Wavefront**

If the light source is linear, a cylindrical wavefront is formed. There will be equidistant points from the source and they will be on a cylinder’s surface.

**Refraction and Reflection of plane waves using Huygens principle**

**Proof of Reflection using Huygens Princip****le**

In the figure, AA’ represents the wavefront incident on a reflecting surface XY with an incidence angle i. According to Huygen’s principle, every point on AA’ will produce secondary wavelets.

Time taken from A’ to D = time taken from B’ to C

**A’D / v = B’C / v**

**A’D = B’C**

**A’C sin(i) = A’C sin(r)**

**Thus, i = r**

Therefore, both the incidence angle and the reflection angle are equal. The first law of reflection also confirms this. In addition, since the incident wavefront AB, the normal wavefront, and the reflected wavefront are all on the same plane, we can also verify the second law of reflection.

**Proof of Refraction using Huygens Principle**

The incidence angle is i, and the refraction angle is r.

From the ΔA1B’B1, we get

**Sin∠B’A1B1 = Sin i = B’B/AB1**

From the ΔA1CB1, we get

**Sin∠A1B1C = Sin r **

**= A1C/AB1**

**Sin i/Sin r = B’B/A1C**

**= v _{1}t/v_{2}t**

**Sin i/Sin r = v1/v2 **

**= 1μ2(constant)**

Snell’s law of refraction is proven here.

The constant ^{1}μ_{2} is called the refractive index of the second medium w.r.t the first medium.

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**FAQs**

##### Light behaves as both a wave and a particle, and under what conditions?

When the light interferes with objects many times bigger than its wavelength, the light behaves as a wave. Once the light is created to move with objects comparable or tiny compared to its wavelength, it behaves as a particle.

##### Why does the sound bend around the corner of a building while light does not?

The wavelength of the light is within the order of 0.5 microns, or 0.0005 millimeters because that light can solely diffract once going through terribly narrow openings. On the other hand, sound waves have a wavelength of the order of one meter and diffract very easily. This enables sound waves to bend around the corner.

##### How does the wavefront propagate?

For a curved plane wave, the wavefront are planes perpendicular to the direction of propagation that moves in this direction alongside the wave.

For more visit Important Topic: Wavefront

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