Young double slits experiment (By pak physics notes) pak physics notes.......

Friday, 18 November 2011

Young double slits experiment (By pak physics notes)

08:00

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.

Arrangement of Experiment

'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.

Experiment

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.

Path difference = BP-AP = BD

S = r2-r1 = BD

In right angled DBAD

Sinq = BD/AB
Or
sinq = s/d
Or
S = dsinq -------(1)

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 :

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)

FOR BRIGHT FRINGE
For bright fringe S = ml -----(3) Therefore, the position of bright fringe is:
_{y = m}_l_L/d

FOR DARK FRINGE AT P
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
FRINGE SPACING
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.
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. (www.pak-physicsnotes.blogspot.com)