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Wednesday, January 23, 2013

Diffraction effect

 Diffration : Sand ball analogy
Consider a sand ball thrown into a open window. If the window size is large in comparison to the dia of the sand ball, the ball will pass undisturbed through the window.If you mount a board so that the ball hits it ofter passing through the window, you will get a single trace on the board.
But, what if the window size is small, comparable to the dia of the ball? Most probably, one or both ends of the ball touch the corners of the window, and eventually those ends of the ball will break apart.So in the board behind the window, you will get a main trace in addition to some small fractions on the board.The pattern of these small traces on the board will depend primarily upon the  nature of the window frame.
Now, in the above picture,replace the sand ball by a light particle and the window by a slit, the board by a screen.The light quanta will break and will yeild a main trace along with some small traces and the pattern of distribution of these traces on the screen will depend upon the shape and size of the slit.

Diffraction is actually Interference !

Diffraction can  be explained technically in terms of interference of light.So lets start from the youngs DS experiment. S1 and s2 are narrow slits placed close together  acting as coherent sources.Let us assume that waves from S1 reaching a particular point P in screen be represented by y1 while Waves reaching same point from S2 be represented by y2
y1 = a1* Sin(wt)
y2 = a2*sin(wt+f)
f is the phase difference at point P.At P , these two waves superpose
y = y1 + y2 = A*Sin(wt +F)
A is the amplitude and F is the phase of the resultant wave at P.
A=√(a12+a22+2*a1*a2*cos(f))
F= tan-1(a2*Sin(f)/(a1+a2*Cos(f)))
A will vary with phase angle f, which in turn will vary with the distance of P from C.At some point A will be maximum(a1+a2), ahile at some nearby points A will be minimum, (a1~a2). Thus as we move along the direction PC, A will keep alternating between Maximim and Minimum values. The points of maximim internsity are called bright fringes while the points of minimum intensity are called dark fringes.here the fringes are of equal width.This pehnomena is known as interference.Here there is a redistribution of light energy on the screen due to two coherent sources placed close together.The width of the dark and bright bands (called fringes) depend on  the following factors
1. Separation between the sources d
2. Separation between the source and screen D
3.Wavelength of light L

Now if the sources are brought infinitesimally close together, will there be interference? Yes, there will be.
If more than two sources are placed infinitesimally close together, then ? Ya, of course, there will be interference, but the fringe pattern will be different.What will happen if such infinite number of infinitesimally thin coherent sources are placed close together, infinitesimal distance apart?There will be interference in this case also, but this last situation resembles a beam of light passing through a not-so-narrow slit.And the fringe pattern that will be observed in the last case will be called a fringe pattern due to diffraction of light through the not so narrow slit.
The fringe pattern will depend uponWidth of the slit , say a, and not on the separation between the individual coherent sources. (the latter being infinitesimally small, becomes insignificant)  and Wavelength of light. Unlike Interference fringes, The Diffraction  fringes are not of equal width, neither of equal internsity and all unequally spaced.
 

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