Refraction using Huygens’ principle

Introduction

We see a variety of objects in the world around us. However, we are unable to see anything in a dark room. When any object reflects the light that is incident on it, this reflected light shows us the object around us. In the world, there are wonderful phenomena related to light such as the twinkling of stars, the colour of the rainbow, etc. 

A light ray is always perpendicular to the light’s wavefront. It is an electromagnetic wave and a narrow beam of light with which light energy travels, this is called a ray of light. When light falls on any object, it is called an incident ray and when this incident ray is reflected by the object, it is called a reflected ray. The direction of light propagation in the second media changes when it is transferred to another transparent medium. By this, we can understand that the light does not travel in the same direction in all media. So, this phenomenon is called the refraction of light.

When an incident ray falls on a medium, the speed changes. In simple words, the speed of light changes when an incident ray enters into a transparent medium from another one.

The Laws of Refraction

The first law stated that the incident ray, the refracted ray and the normal of the transparent media at the point of incidence all should lie on the same plane.

The second law is also known as Snell’s law of refraction. This law stated that the sine of the angle of incidence and the sine of the angle of refraction have a constant ratio.

sin i /sin r= constant  

Where, i is the angle of incident

           r is the angle of refraction.

Note that angle i and angle r are never equal to each other.

This constant value refers to the refractive index of the second medium with respect to the first medium.

Here is a small explanation of refractive index, it is the ratio of the velocity of light in air to the speed of light in a medium. Light travels faster in vacuum when compared to light travelling in the air. Its value depends upon the speed of light in two media.

n = c/v   where, n refers to the refractive index

             c refers to the speed of light in air

              v refers to the speed of light in the medium

The Huygens’ Principle

This rule was discovered by Huygens in 1678 to understand the refraction of light in several mediums.

Before learning about this principle, we have to become familiar with the term “wavefront”. To understand this, let’s take an example. When we drop a small stone in still and calm water, we observe that water waves spread out from the centre of the point of impact. A circular ring forms and all the circular rings are at the same distance from the source. This spherical ring oscillates at the same distance in a phase called wave-front. The wave-front moving outward with a certain type of speed from the source is called the speed of the wave. Note that the energy of a wave always travels in a perpendicular direction to the wave-front.

The Huygens principle allows us to determine the shape of a wavefront at a certain time, T. According to the Huygens principle, each point of the wavefront behaves as the source of the secondary disturbance. And from these points, the wavelet generates and spreads in all directions. A secondary wavelet is when the wavelet is generated from the wave-front. A common tangent is drawn to all these spheres, a new position of the wavefront is obtained at a later time T. So we can say that “Huygens’ principle is that every point of the wavefront acts as a source for a secondary wavelet”. You should know that the sum of spherical wavelets is wavefront.

.F1, F2 represent the spherical wave-front at time zero. G1 and G2 behave as a secondary wavelet which is generated from F1 and F2.Therefore, if we have to find the shape of the wavefront at time T, we have the spheres of radius “vt” from each point. Here, v refers to the speed of the wave. D1 and D2 are considered back or backward waves which do not exist. This back wave is the major argument for the Huygens.

Laws of Refraction Using the Huygens’ Principle

AB represents the surface of separating mediums. v1 and v2 are the speeds of light that are travelling from the first medium to the other one respectively. T is the time taken by a wavefront to cover the distance QR. Now, to find the shape of the wavefront, we have to draw a sphere of radius v2t  from a point P in the second medium. QE is the tangent that is drawn.

Here, PE is v2t and QE is refracted wave-front. Now consider the triangle PQR and PQE.

Sin i = RQ/PQ = v1t/PQ……equation 1

Whereas, sin r = PE/PQ = v2t/PQ….equation 2

By equation one and two, we get

Here are a few limitations of Huygens’ principle

1)  Huygens could not explain why refraction occurs in the first place.

2)  He also could not explain the energy of light when it travels.

3)  However, here is the major limitation of Huygens that he could not explain the fact that in forward direction amplitude of secondary wavelets is maximum, whereas in the backward direction, it is zero.

4)  He was also not able to explain the photoelectric effect.

5)  Also could not able to explain the rectilinear propagation of light      

Sin i / sin r = v1/ v2

Conclusion

We can deduce from the above discussions that if we have to find the shape of a wavefront in optical physics, we have to apply the Huygens principle. As we learned above that it stated, every point of a wavefront acts as a secondary source for the next wavefront. These circular shaped rings are formed at the same distance and travel in the same phase. This principle is used to determine the shape geometrically. It helps us in understanding the propagation of light of classical waves. Here you should also remember that, if the incident angle is bigger than the refracted angle then the speed of light in the second medium will be less than the speed of light in the first medium.