Young's double slit experiment

Young's double slit experiment

Young's in 1801 demonstrated the phenomenon of interference of light by a simple experiment.

S is a narrow slit (of width 1 about 1 mm) lighted by a monochromatic (same color and wave length) source of light of at a suitable distance (about 10 cm) from s, there are two fine slits S₁ & S₂ about 0.5 mm, parallel to S. when a screen is placed at a distance (about 2m) from the slits S₁ & S₂; alternate bright & dark fringes appear on the screen. The fringes disappear when one of the slits S₁ & S₂ is covered.

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Explanation - Young's experiment can be explained on the basis of interference of light. According to Huygens principle, source of light "S" sends out spherical wave fronts. Let the solid arcs represent the crest & dotted arcs represent the troughs. These wave fronts reach the S₁ & S<sub>2 

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Simultaneously, which become sources of secondary wavelets. Thus the two waves of same amplitude & same frequency with zero phase difference are given out by S₁ & S₂. These waves on superposition produce interference. The dots (●) represent the constructive interference & Cross (x) represents destructive interference. Bright & dark fringes are placed alternately & they are equally spaced. These bands are called interference fringes.

Analytical treatment of interference bands-

Calculation of fringe width:-

for bright fringes- 
we know for constructive interference 
                                                     
                                                    
where n= number of fringe which we are considering

Fringe width: - The center to center distance between the dark & dark or bright & bright fringes is called fringe width. It is denoted by "β".

therefore β = x₂ - x₁ or x₃ - x₂       (from above figure)