Interference of waves

Diffraction of waves

Diffraction of waves is a phenomenon in which waves spread out as they pass through an aperture or round a small obstacle. The wave curve round the edges of a obstacle. The amount of curving depends on the relative size of the wavelength of light to the size of the opening. If the opening is much larger than the wavelength, the curving will be almost unnoticeable. However, if the two are closer in size or equal, the amount of curving is considerable, and easily seen with the naked eye.

The effect of diffraction is most obvious when λ ≥ a. This happens when:

  1. the size of the aperture or obstacle, a is small enough,

  2. the wavelength is large enough.

Characteristics of Diffraction of waves:
  1. The frequency, wavelength and speed of the waves remains the same after diffraction.
  2. The direction of propagation and the pattern of the waves change.
  3. The effect of diffraction is most obvious when λ ≥ a, a = size of the aperture.
  4. The amplitude of the part of the wave that spreads out is lower - as the energy is distributed over a bigger area.

Diffraction of water wave    

λ < a

Diffraction through a big aperture. The effect of diffraction is not obvious. The waves are bent only at the edges after passing the slit.

λ ≥  a

Diffraction of a small aperture (about the size of the wavelength of the water wave). The effect of diffraction is obvious. The waves are circular and appear to originate from the small slit.

   The 1st diagram on the left shows diffraction of water wave on a large obstacle. Compare to when it pass through a small obstacle. The effect is more obvious and the waves recombined after passing through the obstacle. Diffraction through a small aperture and a small obstacle. The wave is extended to the shadow region and curve at the edges.

  

 

a = gap size

video clip on diffraction of water wave.

Click and slide the bar to change the size of the slit. Observe the effect of diffraction.

Diffraction of light

Classically, light is thought of as always traveling in straight lines, but in reality, light waves tend to bend around nearby barriers, spreading out in the process. This phenomenon is known as diffraction and occurs when a light wave passes by a corner or through an opening or slit that is the approximate size of, or even smaller than, that light's wavelength. See the pictures on the right.

A very simple demonstration of diffraction can be conducted by holding one's hand in front of a light source and slowly closing two fingers while observing the light transmitted between them. As the fingers approach each other and come very close together, a series of dark lines parallel to the fingers begins to appear.The parallel lines are an example of diffraction patterns.

If you look at a light source through a tiny hole (pin hole) on a piece of cardboard, you will see a bright spot and some bright rings around it, like the one shown below.

Optical effects resulting from diffraction are produced through the interference of light waves. If the crests of two waves combine, an amplified wave (bright fringe) is produced (constructive interference). However, if a crest of one wave and a trough of another wave combine, they cancel each other out to produce no vertical displacement (dark fringes-destructive interference).

Diffraction of light through an obstacle.

Light waves will be diffracted if

  1. light is propagated through a pin hole or a tiny slit where its size is similar to that of the light wavelength (around 10-7m)
  2. the light source must be monochromatic, i.e. light of one colour, and therefore one wavelength.

 

 Diffraction through a slit.

Diffraction pattern through a slit.

 


An example of such a situation is illustrated below in Figure 1, which exhibits the diffraction of sunlight by clouds during sunset, resulting in what is often referred to as their silver lining.

In the atmosphere, diffracted light is actually bent around atmospheric particles -- most commonly, the atmospheric particles are tiny water droplets found in clouds. Diffracted light can produce fringes of light, dark or colored bands. An optical effect that results from the diffraction of light is the silver lining sometimes found around the edges of clouds or coronas surrounding the sun or moon. The illustration above shows how light (from either the sun or the moon) is bent around small droplets in the cloud.

When the wavelength (λ) is much smaller than the aperture width (d), the wave simply travels onward in a straight line, as shown on the left side of Figure 2.

The right side of Figure 2, however, illustrates a different situation. In this case, the wavelength of light transmitted by a point source exceeds the size of the aperture and light is diffracted, with the primary incident light beam landing at point P and the first secondary maxima occurring at point Q. Such a situation results in a diffraction pattern that consists of a bright central portion called the primary maximum flanked on both sides by secondary maxima, which are separated by dark sections known as minima. The secondary maxima decrease in intensity as their distance from the center, the area of highest intensity, increases. The relationship between the size of an aperture and the diffraction that occurs can be demonstrated through the equation:

sin θ = λ/d

where θ is the angle between the incident central propagation direction and the first minimum of the diffraction pattern. Below, Figure 3 further illustrates this point through a plot of beam intensity versus diffraction radius. Note that the minima occurring between secondary maxima are located in multiples of p.

   

 

Look at the picture below. It shows the diffraction of red light. The size of the slit is shown on the right side of the picture.  See how the diffraction patterns differ when the size of the slit decreases. When the size of the slit decreases, there are less bright fringes formed. (λ = ax/D, when a decreases, x increases)

Try out an virtual experiment to see the effect of size of the slit on the diffraction pattern.

Diffraction of sound wave

One is able to hear someone talking around the corner but is not able to see the person; one is able to hear the sound of a siren from an ambulance that pass by but is not able to see the ambulance. This is due to diffraction of sound waves. The wavelength of sound wave is much longer (the wavelength of a note of middle C is 1.3 m) than that of light wave. Therefore the effects of diffraction of sound wave is more obvious. The wavelength of light wave is very small (around 600 nm) compare to the size of aperture or obstacle. Hence the effect of diffraction of light is not noticeable.

                                       

Siren is always sound of low frequency in order that its wavelength is long. If wavelength is long and almost the same as the size of an obstacle, sound can be diffracted more. Siren would be heard around the corner or inside a building.


Application of diffraction of water waves

Construction of a wall with a gap at the sea front of a harbour to protect the port from being hit by large waves.

Once the sea wave pass through the aperture of the harbour wall, they are diffracted and begin to spread out into curved waves. As they spread out, their amplitude is reduced. The power of the waves which have been allowed into the harbour are spread out throughout the whole enclosed space of the harbour walls. This means that any boat or ship floating within the harbour only experiences very small (dissipated) waves, despite that fact that the inner water is exposed to the outside waves through the small gap in the harbour wall. Hence the sea near the harbour is calmer and safer.

 

 

 

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