Monday, February 18, 2008

DIFFRACTION OF LIGHT

Diffraction of light
When a narrow slit AB is placed in the path of light, then only part A’B’ of the screen should be illuminated and no light should enter the geometrical shadow regions A’X and B’Y of the screen. On the other hand, when obstacle AB is placed, then its distinct geometrical shadow is A’B’.
It happens exactly so only when the size of the slit or obstacle is large. However, if the size of the obstacle is made small, of the order of wavelength of light used, then light enters into the geometrically prohibited regions showing thereby that light bends round the corners of the slit or obstacle.
This phenomenon of bending of light round the corners and spreading of light into the regions of geometrical shadow is called diffraction.
Fresnel and Fraunhoffer diffraction
Based on the relative positions of the source and screen with respect to the object causing diffraction, we have two classes of diffraction-Fresnel and Fraunhoffer.
In fresnel diffraction, either the source of light or the screen or both are at finite distances from the obstacle causing diffraction. Here to get the diffraction effect on the screen, no modification is made by lenses and mirrors.
Example: Diffraction at a single slit
In Fraunhoffer diffraction, both the source and screen are at infinite distances from the object causing diffraction. In actual practice, the source and the screen are placed at the focal planes of two convex lenses. Then both the source and image(screen) are effectively at infinity.
Diffraction Grating
An arrangement which is equivalent in action to a number of parallel,euidistant,narrow rectangular slits of equal width placed side by side is called diffraction grating.
Gratings are made by ruling equidistant parallel lines on an optically transparent sheet of material, the line portion being opaque and the space between the lines being transparent to light. This sheet acts as a transmission grating. To get a reflection grating, lines are drawn on a plane silvered surface.
In the construction of good quality grating, the following considerations must be taken into account.
(1) It should have large number of slits (the number of lines should be large).
(2) The spacing between the lines should be equal.
Original gratings are quite expensive. Hence their photographic reproductions or replicas are used.
Theory
Let XY represent a plane transmission grating. AB represent an opaque portion and BC a slit. Let ‘a’ be the width of each slit and ‘b’ the width of an opaque portion. The distance (a+b) is called the grating element.
Let a parallel beam of monochromatic light of wavelength l be incident normally on the grating surface. Most of the light go go straight, but a part of it gets diffracted. When focused by a convex lens L, maximum intensity is observed at P, the focus of the convex lens.
Since the width of the slit is of the order of wavelength of light, part of the light get diffracted at the slit, in different directions. Consider the secondary waves originating from A and C proceeding at an angle q with the normal. The path difference between the waves on reaching the point O is,
AN = (a+b) sinq
Condition for maximum intensity, (a+b) sinq = nl
If there are N lines/meter in a grating, a+b = 1/N
\sinq = nNl ----- (1)
This is known as grating equation.
Intensity distribution of diffraction pattern
P corresponds to the position of central maximum and 1, 2 etc. on the two sided of P represent the 1st, 2nd etc. principal maxima. a,b,c etc. are secondary maxima and d,e etc. are secondary minima.

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