Diffraction

The bending of light from the corners of bostacle placed in path and spreading of light to the geometrical shadow is called comparable with the wavelength of light used then diffracted rays will overlay and results the diffraction fringe called as secondary minima and secondary maxima
Types od Diffraction
1) Freshel's diffraction: When diffraction is observed placing source or screen or both of them at a finite distance from slit. Then this is called as Fresnel's diffraction
2)Frauhafer diffraction
when source and screen are placed at infinte distance from slit and diffraction is observed then this types of diffraction is called fraunhofer diffraction. Lenses are used to observe this type of diffraction

Diffraction through Single slit
Let a parallel beam of light be incident on a slit of widtha then beam will be diffracted and we can observe a diffraction pattern on the screen, When slit width a is comparable with wavelength diffraction fringes can be observed.

Principal maxima: At the centre point of screen all the wave from slit will reach is same phase i.e path difference will be zero and hence intensity will be maximum or bright fringe occurs and called as principla maxima

Secondary minima
Let us consider lamda be the wavelength of the light used and a be the width of the slit. Now, divide the slit into two equal halves. Then taking waves travelling at an angle theta towards screen. Then path difference between 1st and 2nd wave will be
S2N = S1S1sintheta
= a/2 * sintheta

path difference = a/2 sin theta

If this path difference is ewusl to lamda/2 then dark fringe occurs.
i.e a*2 * sin theta = lamda/2
asin theta = lamda---------------1
Now if the slit is divided into four equal parts then path difference will be qual parts, then path difference will be equal to a/4 sin theta and dark fringe would occur if
a/4 * sin theta = lamda/2
a= sintheta = 2 lamda ------------2
and so on
asin theta = n lamda-----------------3
n = 1,2,3...................
FOr first secondary minima
asin theta = lamda
2nd secondary minima, asin theta = 2 lamda

Secondary maxima
When the slit is divide into three equal parts and two consecutive wave calcels effect6s of eath other and third remains unaffrected and gives bright fringe i.e
For first secondary maxima,
asin theta = 3/2 * lamda
2nd secondary maxima
asin theta = (2n+1)/2 * lamda
n= 1,2.........



Diffraction through double slit
Let us consider AB and CD be two identical slits having width a separated by an opaque BC of width b. Let a beam of monochromatic light be incident on the slits then interference and diffraction pattern can be observed on the screen.

Interference maxima and minima
At the centre of screen all the waves will meet in same phase so, this point will be of maximum intensity and called as principal maxima.
DIagram

Every point on the slit behaves as secondary wave source. Consider the central points of eath slits as source such that they will be coherent. If we take wave moving at anglr theta towards screen then path difference between these two S2N.
S2N = S1S2sintheta
=(a+b)sintheta

Now, interference maxima would occur if (a+b)sin theta = n lamda and interference minima would occur if
(a+b)sin theta = (2n+1)/2 * lamda


Diffraction maxima and minima
Let us consider two waves diffrented from upper edge of each slit moving at an angle theta towards screen. Then path difference between these two will be
S2N = S1S2 sin theta
=(a+b) sin theta

Diffraction maxima would occur if
(a+b) sin theta = n * lamda
and Diffraction minima would occur if
(a+b)sin theta = (2n+1)/2 * lamda


Diffraction grating
It is an arrangment of larger number of ruling ina glass plate of 1 inch in which the ruled lines behaves as opaque portion and glass left between each two line behaves as slit. Generally there are around 2000 lines in a glass plate of 1 inch.
If ruling is made on a transparent glass plate, the it is called a plain transmission grating and if it is made on a mirror then it is called as reflection grating. Here, combination of a single slit and a single opaque is called as grating element
If N be the no. of lines in a glass plate of one inch and a and b be the width of slit and opaque portion then
Na+Nb = 1 inch
(a+b) = 1/N inch = 2.54/N cm