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Fraunhofer diffraction by a single slit is considered one the most difficult concept.
20 Questions around this concept.
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s doubleslit experiment is
Fraunhofer diffraction by a single slit
let's assume a plane wave front is incident on a slit AB (of width b). Each and every part of the exposed part of the plane wave front (i.e. every part of the slit) acts as a source of secondary wavelets spreading in all directions. The diffraction is obtained on a screen placed at a large distance. (In practice, this condition is achieved by placing the screen at the focal plane of a converging lens placed just after the slit).
Secondary minima : For obtaining nth secondary minima at P on the screen, path difference between the diffracted waves
2. Distance of nth secondary minima from central maxima:
where D = Distance between slit and screen.
= Focal length of converging lens.
Secondary maxima : For nth secondary maxima at P on the screen.
Path difference ; where n = 1, 2, 3 .....
(i) Angular position of nth secondary maxima
(ii) Distance of nth secondary maxima from central maxima:
Central maxima : The central maxima lies between the first minima on both sides.
(i) The Angular width d central maxima =
(ii) Linear width of central maxima
Intensity distribution: if the intensity of the central maxima is then the intensity of the first and secondary maxima are
found to be . Thus diffraction fringes are of unequal width and unequal intenstities.
(i) The mathematical expression for in intensity distribution on the screen is given by:
where is just a convenient connection between the angle that locates a point on the viewing screening and light intensity I.
Phase difference between the top and bottom ray from the slit width b.
Also .
(ii) As the slit width increases relative to wavelength the width of the control diffraction maxima decreases; that is, the light undergoes less flaring by the slit. The secondary maxima also decreases in width and becomes weaker.
(iii) If b>>λ, the secondary maxima due to the slit disappear; we then no longer have single slit diffraction.
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