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YOUNG'S
DOUBLE SLIT EXPERIMENT
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| The first practical demonstration of optical interference was provided by THOMAS YOUNG in 1801. His experiment gave a very strong support to the wave theory of light. | |||
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EXPERIMENTAL
ARRANGEMENT
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| 'S' is a slit, which receives light from a source of monochromatic light. As 'S' is a narrow slit so it diffracts the light and it falls on slits A and B. After passing through the two slits, interference between two waves takes place on the screen. The slits A and B act as two coherent sources of light. Due to interference of waves alternate bright and dark fringes are obtained on the screen. | |||
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QUANTITATIVE
ANALYSIS
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| Let
the wave length of light = l Distance between slits A and B = d Distance between slits and screen = L Consider a point 'P' on the screen where the light waves coming from slits A and B interfere such that PC=y. The wave coming from A covers a distance AP=r1 and the wave coming from B covers a distance BP=r2 such that PB is greater than PA. For latest information , free computer courses and high impact notes visit : www.citycollegiate.com |
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Path
difference = BP-AP = BD
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S = r2-r1 = BD
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| In right angled DBAD | |||
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Sinq
= BD/AB
Or sinq = s/d Or S = dsinq -------(1) |
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| Since the value of 'd' is very very small as compared to L, therefore, q will also be very small. In this condition we can assume that : | |||
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Sinq = tanq
From (1) S = dtanq ---(2) In right angled DPEC Tanq = PC/EC = y/L Putting the value of tanq in eq. (2), w get S = dy/L Or y = SL/d -----(3) |
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FOR
BRIGHT FRINGE
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| For
bright fringe S = ml -----(3) Therefore, the position of bright fringe is: |
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y
= mlL/d
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FOR
DARK FRINGE AT P
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| For
destructive interference, path difference between two waves is (m+1/2)l
----(3) Therefore, the position of dark fringe is: y = (m+1/2)lL/d |
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FRINGE
SPACING
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| The
distance between any two consecutive bright fringes or two consecutive dark
fringes is called fringe spacing. Fringe spacing or thickness of a dark fringe or a bright fringe is equal. It is denoted by Dx. |
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Consider
bright fringe.
y = mlL/d For bright fringe m=1 y1 = (1)lL/d for next order bright fringe m=2 y2 = (2) lL/d fringe spacing = y2 - y1 or Dx = (2)lL/d - (1)lL/d Dx =lL/d (2-1) Dx = lL/d Similar result can be obtained for dark fringe. |
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| For latest information , free computer courses and high impact notes visit : www.citycollegiate.com | |||