 # Huyghen's principle and interference of light

## 9)Young Double slit experiment

• 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 S1 and S2 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 S1 and S2 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 S1 or S2 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.

## 10) Theory of interference fringes

• 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 S1 or S2 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,S1 or S2
• 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 S2P-S1P
• from figure (6) for x, d<<< D , S1P+S2P =2D
with negligible error included , path difference would be And corresponding phase difference between wave is i) Condition of bright fringes(constructive interference)
• If the path difference (S2P-S1P) is even multiple of λ/2,the point P is bright • Equation (21) gives the condition for bright fringes or constructive interference
ii) Condition for dark fringes (destructive interference)
• If the path difference is an odd multiple of λ/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 β. Thus 