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### 4.2 Interference

Firstly, a short definition on the coherence of the waves, two waves(of same type) are said to be coherent if there is a constant phase difference between them (same frequency implied) and of same amplitudes. For e.g. as the following plots shows two waves with a constant phase difference,

Now, Interference is the terms referred to the result of superposing two or more waves of the same types. The conditions for the visible and definite interference pattern to be observed are as follows,
• The waves must be coherent. If the waves that interfere are not coherent, the interference patterns would form but not in definite pattern we would otherwise desire.
• The waves must approximately have the same amplitude. If the amplitudes varies then neither the constructive nor the destructive interference could occur and the even if it did interefere the pattern may not have sufficient contrast to be observed.
• Interference can only occur between wave disturbances oscillating in the same plane. For transverse waves, they must be either unpolarized or polarized in the same plane.

YOUNG'S DOUBLE SLIT EXPERIMENT:

"A double-slit experiment was performed originally by Thomas Young in 1801. He believed it demonstrated the validity of wave theory of light.It is in this respect his experiment is sometimes referred to as Young's experiment or Young's slits. The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. The modern version of the experimental setup is as shown below."-wikipedia
Explanation: Light from the monochromatic source is passed through a double slit, as shown above. The light from the double slit acts as a two different sources and thus superpose on the screen with alternate constructive and the destructive interference resulting in the fringe pattern on the screen. It is impotant that monochromatic light has to be used because white light is composed of a spectrum of wavelengths. If we use whitelight then a spectrum of pattern will be produced. The figure below shows us, how it looks from above.

The following is the enlarged version of the above. Where we have only take two fringes,

If $D>>x$ then, the wavelength($\lambda$) of the monochromatic light is given by,
$$\lambda=\frac{ax}{D}$$
where, $a=$double slit separation in meter($m$), $x=$fringe spacing in meter($m$) and $D=$distance between the slit and the screen in meter($m$).

Here's an explanation of original Thomas Young's experiment,

Examples:  A beam of light consisting of  wavelenghts 600 nm is used to obtain interference in Young's Double Slit experiment (YDSE). Find the fringe separations if the distance between the two slits is 0.4 mm and screen is placed at a distance of 1.0 m from the slits. Ans:$1.5mm$