Refraction and Reflection of Waves Using Huygen’s Principle

As we know that when light falls on an object, it bends and move through the material, this is what refraction is. Also when the light bounces off the medium it is called a reflection. Let us know study reflection and refraction of waves by Huygen’s principle.

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Reflection using Huygens Principle

We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface.  Plane AB is incident at an angle ‘ i ‘ on the reflecting surface MN.  As these rays are incident from the surface, so we call it incident ray. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.

These incident wavefront is carrying two points, point A and point B, so we can say that from point B to point C light is travelling a distance. If ‘ v ‘ represents the speed of the wave in the medium and if ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance

BC = vr

In order the construct the reflected wavefront we draw a sphere of radius vr from the point A. Let CE represent the tangent plane drawn from the point C to this sphere. So,

AE = BC = vr

If we now consider the triangles EAC and BAC we will find that they are congruent and therefore, the angles ‘ i ‘ and ‘r ‘ would be equal. This is the law of reflection

Browse more Topics under Wave Optics

• Coherent and Incoherent Addition of Waves
• Diffraction
• Huygens Principle
• Interference of Light Waves and Young’s Experiment 
• Polarisation

Refraction using Huygen’s principle

We know that when a light travels from one transparent medium to another transparent medium its path changes. So the laws of refraction state that the angle of incidence is the angle between the incident ray and the normal and the angle of refraction is the angle between the refracted ray and the normal.

The incident ray, reflected ray and the normal, to the interface of any two given mediums all lie in the same plane.  We also know that the ratio of the sine of the angle of incidence and sine of the angle of refraction is constant.

We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface. As these rays are incident from the surface, so we call it incident ray.

Let PP’ represent the medium 1 and medium 2. The speed of the light in this medium is represented by v₁ and v_2. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.

If  ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance,

BC = v₁ r

So to determine the shape of the refracted wavefront, we draw a sphere of radius v₂r from the point A in the second medium. Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v₂r, and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain

sin i = \( \frac{BC}{AC} \) = \( \frac{v_1r}{AC} \)

sin r = \( \frac{AE}{AC} \)= \( \frac{v_2r}{AC} \)

where’ i ‘ and ‘ r ‘ are the angles of incidence and refraction, respectively. Substituting the values of v₁ and v₂ in terms of we get the Snell’s Law,

n₁ sin i = n₂ sin r

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Solved Question for you on Reflection and Refraction of light using Huygens Principle

Q. The phase change in reflected wave, when lightwave suffers reflection at the interface from air to glass is

1. 0
2. π/2
3. π
4. 2π

Answer: C. When a light is reflected from denser to rarer medium, there is no phase change in the light but when a light is reflected from rarer to denser medium, there is a phase change of π. So, here the air is rarer than glass and there is a phase change of π.