1800-1023-196

+91-120-4616500

# Refraction and Reflection of Plane waves using Huygens’s Principles

## Refraction of a Wave

Refraction is defined as bending of light wave when it passes from one medium to other. Like reflectionrefraction also occurs for other types of waves like sound, water etc. The amount of bending of light depends upon the change in speed of light and the angle at which the light ray falls on the surface. For Example, the eye’s natural lens bends rays of light.We are not able to focus light onto the retina without the bending of lightRefractive Index is the ratio of velocity of light in vacuum to the velocity of light in the medium, µ = c/v.

The laws of refraction states that the incident ray, the refracted ray and the normal drawn perpendicular lie in the same plane. The ratio of sine of angle of incidence and angle of refraction is a constant. This is called Snell’s Law of Refraction. Snell’s law states that µ 1SinƟ1 = µ 2SinƟ2. Here µ1 is the refractive index of medium 1 and µ 2 is the refractive index of medium 2. Ɵ1 is the angle of incidence and Ɵ2 is the angle of refraction. When the ray of light passes from rare medium to denser medium, the refracted ray inclines closer to the normal in denser medium. If the light ray goes from denser medium to rarer medium the refracted ray departs away from the normal.

 Laws of Refraction Light travelling from denser medium to rarer medium

## Reflection of a Wave

Reflection of a wave is the process by which the light wave strikes an object and bounces back. This process occurs for not only light waves but also for sound waves, infrared or radio waves. If the light falls on a smooth and clear surface, the light rays reflect back at the same angles. This type of reflection is called Specular Reflection. The light which reflects back from the surface of a mirror is specular reflection. When the light rays hits on a surface of imperfections, it bounces back at different angles. This is called Diffuse Reflection.

Law of reflection describes the behavior of light waves when it strikes on a surface. Consider a mirror surface. The light wave which moves towards the surface is called Incident Ray. After hitting the surface the light wave which bounces back is called the reflected ray. Now consider the point where the ray is incident on the surface. Then draw a line which will be perpendicular to the surface of the mirror. The line which is drawn is called Normal Line. The normal line divides the angle into two equal angles between the incident ray and the reflected ray. These two angles will be the angle of incidence and angle of reflection. Thus the law of reflection states that the angle of incidence is equal to the angle of reflection. Also the incident ray, the reflected ray and normal which is drawn at the point of incidence, all lie in the same plane.

Laws of Reflection

These two optical phenomena can be considered in the formation of rainbow. Both refraction and reflection work within a rainbow. Light is refracted when the sunlight enters into the water drop. Thus the rays bend at different angles depending on the wavelength of light. Then some of the light will reflect off the back of the drop and again passes back into the air. The light is again refracted when it leaves the drop. Thus the formation of rainbow occurs.

 Formation of Rainbow (a) Formation of Rainbow (b)

## Huygens’s Principle

Huygens proposed the wave theory of light. He suggested that light travels in the form of waves. Huygens’s principle states that each and every point of a wavefront act as a source of secondary and release secondary spherical wavelets of light. These secondary wavelets transmits with the velocity of light in the same medium. A wavefront is a real or imaginary surface where the phase of oscillation is the same. Huygens’s principle of wave theory of light is used to prove the laws of reflection and laws of refraction.

## Refraction of plane wave using Huygens Principle

The velocity of light changes when passes from one medium to another. This bending of light wave when it enters into other medium is called Refraction

As per the diagram shown below consider a plane wave front AB which is incident on the surface. Let v1 and v2 be the velocities of the incident ray and refracted ray of medium 1 and medium 2 respectively (v1>v2).The velocity of the waves depends upon the medium. From Huygens’s principle A and C forms the source of secondary spherical wavelets. Let t be the time taken from B to reach C.

So BC = v1t in medium 1

To determine the shape of the refracted wavefront, we draw a sphere of radius v2t from the point A in the second medium. It denotes the secondary spherical wavefront at time t.

AD = v2t in medium 2.

Now CD is the tangent drawn from point C to the sphere. Thus AD and CD are the refracted wavefronts.

Illustration of Refraction laws based on Huygens’s principle

Sin i / Sin r = (BC/AC) / (AD/AC)

= v1t/v2t

= v1/v2

= µ which is a constant. µ is the reflective index of the medium.

Refractive Index is the ratio of velocity of light in vacuum to the velocity of light in other medium.

Hence Snell’s Law of refraction is proved using Huygens’s principle. Also the incident wavefront, the refracted wavefront and the normal lie in the same plane.

## Reflection of a plane wave using Huygens Principle

As discussed earlier, when light is incident on the surface it is re- emitted without any change in the frequency. This re-emitted light which is returned into the same medium from which it comes out is called Reflection of Light. Consider the figure given below:

Imagine incoming rays are incident on a surface. Here the wavefronts are plane waves. In plane wavefront, the wavefronts will be infinite parallel planes to each other with constant amplitude. Consider the plane wave AB which falls on the reflecting surface. AB is the incident wavefront and is drawn as perpendicular to the incident ray. It falls at an angle i on the surface. Now according to the Huygens’s principle every point on AB act as a source of secondary wavelets. Consider the points A and B as new sources which emits the secondary waves. The velocity of the propagation of waves is ‘v’. Let ‘t’ be the time taken. So let’s assume that vt be the distance moved by the secondary wavelets. AA1 and BE are the secondary waves. Now the new wavefront should be a tangents line which connects those two secondary waves. The reflected waves should be perpendicular to the new wavefront. A1E is the new tangential line which connects the secondary wavelets.

Illustration of Reflection laws based on Huygens’s principle

Consider ΔABE and ΔAA1E. Here AE is common.

<B = <A= 90° .

AA= BE.

These triangles are congruent triangles

So   <i = <r

Thus Angle of Incidence = Angle of Reflection. This is the first law of reflection.

The incident wavefront, the reflected wavefront and normal lie in the same plane which is perpendicular to the reflecting surface. This again verifies the second law of reflection. Therefore, the two Laws of Reflection are verified using Huygens’s Principle.

## Summary

• Refraction is the bending of waves when passes through a different medium.
• Reflection is the process in which light waves falls on a surface and bounces back.
• In refraction, the sine of angle between the incident ray and normal maintains a constant ratio with the sine of angle of refracted ray and normal. Snell’s Law of refraction is proved using Huygens’s principle
• The incident ray, the refracted ray and the normal to the refracting surface lie in the same plane.
• The laws of reflections are verified using Huygens’s Principle. The incident ray, the reflected ray and normal to the reflecting surface lie in one plane which is perpendicular to the reflecting surface. The angle of incidence equals angle of reflection.

Watch this Video for more reference