Huygens’ Principle

Understanding and using Huygens’ principle with wave propagation

- Zeanna Janmohamed

overview

• The principle states that every point on a wave front is the source of a wavelet– These wavelets will spread out in a forward

direction at the same speed as the inception wave – The new wave front will be a line tangent to the

wavelet

Figure 1.0 wavelets in water http://thumbs.dreamstime.com/t/drop-water-4865181.jpg

History and overview

• Christian Huygens was a 17th century Dutch scientist – In 1678 he proposed that the sum of secondary

waves which are the result of disturbance determines the form of the new wave

– He derived the laws of reflection and refraction but could not explain diffraction • This was later added to by Augustin-Jean Fresnel

History and overview cont.• Recognized that the

propagation of a wave could be described by considering a point on a wave

• Result wave can be determined by adding all the values from the point sources

Figure 1.1 straight wave front: each point emits a semicircular wavelet https://www.boundless.com/physics/textbooks/boundless-physics-textbook/wave-optics-26/diffraction-175/huygens-principle-636-5593/

How to use Huygens’ principle

1. Draw a spherical wave Select equal speed points around the wave

2. Draw circles from different points along the wave that have centers at different points along the initial wave front This way the outer edges of the circles will overlap slightly

3. Draw tangent lines to the individual circular wave front

Huygens’ principle – why is it important

• Huygens’ principle of diffraction can be related to the equation d=vt (where d=distance, v = propagation speed, and s=time)

• This means that each wave fronts emits their own v – Emitted waves are semi circular as shown from the

previous side– Principle works for all waves and can describe

interference and refraction

examples

• Imagine walking beside someones room in residence, they are watching a movie and their door is closed. Can you hear it too well? – Probably not

• What happens when the person’s door is open though? – You can hear it not only in front of their room but along the

hall too! • This is a direct result of diffraction, because waves bend

in the tangent lines. Similarly light does the same thing and can be used to understand the basic concept of diffraction

Plane waves• Plane waves have wave front that lie in planes

that are parralel to one another

Figure 1.2 plane wave anatomy http://commons.wikimedia.org/wiki/File:Plane_Wave_Oblique_View.jpg

Examples of plane waves

• This is what we see in waves themselves – Once created, a plane wave can continue to

progragate as a plane wave • If the wave extends in a horizontal direction the viritcal

distance shows the amplitude of the wave

Figure 1.4 wave fronts http://www.ualberta.ca/~pogosyan/teaching/PHYS_130/images/500px-Plane_wave_wavefronts_3D.svg.png

Test your understanding

• Question: using Huygens’ princple explain the diffraction of waves in water in a ripple tank as these waves pass through a slit in the barrier. – See next slide for answer

Figure 1.4 a ripple tank set up http://upload.wikimedia.org/wikipedia/commons/thumb/a/af/Simple_ripple_tank.svg/2000px-Simple_ripple_tank.svg.png

Answer to testing

• Because each point on the initial wave front plane that enters the slit will act as a source of a secondary wavelet, the wavelets will disperse in all directions after the slit causing the waves to spread into regions beyond those in line with the given slit.