Young's Double Slit Experiment - Division of the wavefronts

Thomas Young was the first who observed the interference of light in 1801. He placed monochromatic source of light in front of a single slit. In order to get a coherent light he placed another two slits very close to each other in front of the first one. After passing light rays from the two slits a pattern of alternate dark and bright fringes is formed on a screen placed parallel to slits at some distance.The central fringe was bright. From the interference of light we can easily calculate the wavelength of the light.
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  Simple ray geometry of Young's double slit experiment  

      The above figure shows the experimental arrangement, similar to that devised by Young in 1801, for studying interference effect of light. A screen having two narrow slits is illuminated by a beam of monochromatic light. The portion of the wavefront incident on the slits behaves as a source of secondary wavelets (Huygen's principle). The secondary wavelets leaving the slits are coherent. Superposition of these wavelets result in a series of alternate bright and dark fringes which are observed on a second screen placed at some distance parallel to the first screen.

Interference Of Light Waves

"Superposition of two light waves having phase coherence traveling in the same direction results in a phenomena called Interference."
Light from a Source S passes through a pinhole and falls on two further pinholes A and B, light and dark fringes appear on the screen where the resultant pencils of light overlap. The pencils of light interfere and produce "Interference fringes", first observed by Thomas Young in 1801. These and similar fringes were used by Fresnel and Young to establish the wave theory of light.
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  Fig   Young's Double slit Experiment for Interference

        When two waves are allowed to superpose upon each other and, if the resultant intensity of the interfering waves is zero or less than the intensity of the either individual wave then this type of interference is called "Destructive Interference" and it occurs where crest of one wave falls upon trough of other wave.

       Similarly, if the resultant intensity of the interfering waves is greater than the intensity of an individual wave then this type of interference is known as "Constructive Interference" and this occurs where crest of one wave overlaps the crest of other wave or trough of one wave overlaps the trough of other wave.

       

Essential Conditions for the Interference:

         Interference of light waves is not easy to observe because of the random emission of light from a source. The following conditions must be met, in order to observe the phenomena:

1- The interfering beams must be monochromatic that is, of a single wavelength.

2- The interfering beams must be coherent.

Coherent: waves that are in phase both temporally and spatially. Most practical radiation sources are not coherent over an appreciable length of time since waves trains of limited length are emitted at random intervals. The laser is a source of coherent radiations.

      Consider two or more sources of light waves of the same wavelength. If the sources send out crests or troughs at the same instant, the individual waves maintain a constant phase difference with one another. The monochromatic sources of light which emit waves, having a constant phase difference are called coherent source.

     A common method of producing two coherent light beams is to use a monochromatic source to illuminate a screen containing two small holes, usually in the shape of slits. The light emerging from the two slits is coherent because a single source produces the original beam and two slits serve only to split it into two parts. The points on Huygen's wavefront which send out secondary wavelets are also coherent sources of light.

"In an Interferometer, fringes are produced and used to make accurate measurement of wavelength."

Huygens's Principle

A wave theory of light based on the concept of wavelets or secondary waves spreading from each point affected by a disturbance and conspiring to give a fresh wavefront which envelops the wavelets which create it. The amplitude in a secondary wavelet falls off in proportion to ( 1 + Cosθ ), where θ is the angle with the forward direction. Huygens conceived the waves as longitudinal in nature and could not explain polarization.
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         Knowing the shape and location of a wavefront at any instant t, Huygen's principle enables us to determine the shape and location of the new wavefront at a later time t + ∆t. This principle consists of two parts: 

 Every point of a wavefront may be considered as a source of secondary wavelets which spread out in forward direction with a speed equal to the speed of propagation of the wave.

The new position of the wavefront after a certain interval of time can be found by constructing a surface that touches all the secondary wavelets.

     The principle is illustrated in Fig 1 given below. AB represent the wavefront at any instant t. To determine the wavefront at time t + ∆t, draw secondary wavelets with center at various points on the wavefront AB and radius as c∆t where c is the speed of the propagation of the waves as shown in Fig 1. The new wavefront at time t + ∆t is A'B' which is a tangent envelope to all the secondary wavelets. Fig 2 shows a similar construction for a plane wavefront.

  Fig 1 . Spherical Wavefront                      Fig 2 . Plane Wavefront 

Wavefronts

The surface over which particles are vibrating in the same phase. The surface is normal to rays in isotropic media.
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Isotropic: A body is isotropic if its properties are the same in all direction

       Consider a point source of light as S ( Figure given below ). Waves emitted from this source will propagate outwards in all directions with speed c (c is the speed of light). After time t, they will reach the surface of a sphere with center as S and radius ct. Every point on the surface of this sphere will be set into vibration by the waves reaching there. As the distance of all these points from the source is the same, so their state of vibration will be identical. In other words we can say that all the points on the surface of the sphere will have the same phase.

Phase: Particles in periodic motion due to the passage of a wave are said to be in the same phase of vibration if they are moving in the same direction with the same relative displacement. Particles in a wavefront are in the same phase of vibration and the distance between the phases are the same is the wavelength i.e λ.

   Fig  . Spherical wavefronts

Such a surface on which all the points have the same phase of vibration is known as wavefronts.

         Thus in case of a point source, the wavefront is spherical in shape. A line normal to the wavefront including the direction of motion is called a ray of light.

          With time, the wave moves farther giving rise to new wave fronts. All these wavefronts will be concentric spheres of increasing radii as shown in the figure given above. Thus the wave propagates in space by the motion of the wavefronts is one wavelenth. It can be seen that as we move away at greater distance from the source, the wavefronts are parts of spheres of very large radii. A limited region taken on such a wavefront can be regarded as a plane wavefront ( Shown in figure given below ). For example, light from the sun reaches the Earth in plane wavefronts.

   Fig  . Plane wavefronts

      
       In the study of interference and diffraction, plane waves and plane wavefronts are considered. A usual way to obtain a plane wave is to place point source of light at the focus of a convex lens. The rays coming out of the lens will constitute plane waves.