- Introduction
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- Wave fronts and rays
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- Huygens’s principle
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- Reflection of and Refraction of plane waves using Huygens’s principle
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- Principle of Superposition of waves
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- Interference of light waves
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- Coherent Sources
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- Conditions for sustained interference of light waves
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- Young Double slit experiment
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- Theory of interference fringes
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- Displacement of fringes

- Young in 1801 demonstrated interference phenomenon through double slit experiment

- In his experiment ,he divided a single wave front into two and these two slit wave fronts acts as if they emerged from two sources having fixed relationship

- when these two waves were allowed to interfere ,they produce a sustained interference pattern

- In his original experiment he illuminates a pin hole S using a light source and light diverging from pinhole which contains two sets of pinholes S
_{1}and S_{2}equidistant from S and very close to one another as shown below in the figure

- Two two sets of spherical waves coming out of the pin holes S
_{1}and S_{2}were coherent and interfered with each other to form a symmetrical pattern of varying intensity on screen XY

- This interference pattern disappear when any one of the pinholes S
_{1}or S_{2}is closed

- Young used the superposition principle to explain the interference pattern and by measuring the distance between the fringes he managed to calculate the wavelength of light.

- In young's double slit experiment ,light wave produce interference pattern of alternate bright and dark fringes or interference band

- To find the position of fringes, their spacing and intensity at any point P on screen XY .Consider the figure given below

- Here S
_{1}or S_{2}two pin holes of YDS interference experiment and position of maxima and minima can be determined on line XOY parallel to Y-axis and lying on the plane parallel to S,S_{1}or S_{2}

- Consider a point P on XY plane such that CP = x.The nature of interference between two waves reaching point P depends on the path difference S
_{2}P-S_{1}P

- from figure (6)

for x, d<<< D , S_{1}P+S_{2}P =2D

with negligible error included , path difference would be

And corresponding phase difference between wave is

- If the path difference (S
_{2}P-S_{1}P) is even multiple of Î»/2,the point P is bright

- Equation (21) gives the condition for bright fringes or constructive interference

- If the path difference is an odd multiple of Î»/2,the Point P is dark. So,

- Equation (22) gives the condition for dark fringes or destructive interference

- From equations (21) and (22) ,we can get position of alternate bright and dark fringes respectively

- Distance between two consecutive bright fringes is given by

- Thus the distance between two successive dark and bright fringes is same. This distance is known as fringe width and is denoted by Î². Thus