Diffraction Note | Class 12 Physics | NEB | NEPALI EDUCATE

Introduction:

The phenomenon of bending of light waves into the reason of geometrical shadow is called Diffraction.

The diffraction of sound waves is easily noticed in our daily life but not light waves it is because the wavelength of sound waves is comparable with the ordinary object but not the light wave. It means that the amount of diffraction of waves depends upon size of obstacles and Wave length of the sound waves.

Fraunhofer's diffraction through a single sheet:

Let us consider a monochromatic source of light kept at the focus of lens L₁ from where the rage becomes parallel and incident upon single slit of with(d). The secondary wavefront diffracted at the slit is forecast on the screen with the help of lens L₂.

At the center of the screen the brightest pattern is obtained followed by another bright pattern of decreasing intensity on either side. The path difference of secondary waves meeting at the Centre of the screen is zero. So, a bright pattern is obtained called Central Maxima.

Suppose the secondary wavefront at the slit diffract at angle Θ and focused at point P on the screen by the lens L₂. P will be either bright or dark depending upon the path difference from the figure.

x =BN = dSinΘ ........(1)

Secondary Minima:

If d SinΘ = λ, then
The secondary wavefront at the slit can be divided into two equal halves in such a way that these two halves meet at point P destructively as their path difference is λ/2.

dSinΘ₁= λ is the condition for first minima.

If BN =2 λ, the secondary wavefront at the sleet can be divided into four equal halves in such a way four halves meet at point P destructively. In figure the secondary waves are portion AE and EF meet at point P destructively the wavefront in portion A,B destructively.

dSinΘ₂= nλ is the condition for second minima.
∴dSinΘn= nλ

[Condition for nth minima]

Secondary Maxima:
If BN =   , then

Wavefront and slit can be divided into three equal halves as shown in the figure.
The two halves at the slit meet destructively at point P on the screen leaving 3rd on destruct which form first secondary maximum.

∴ dsinΘ=  

In general,

dsinΘ= (2n+1)

Is the condition for n^th secondary maxima.

The diffraction pattern obtained on the screen as the brightest image at the Centre which is followed by the secondary maxima of decreasing intensity on either side with a central Maxima
let us consider the lens of a focal length (f) is placed very close to the slit a b as shown in figure.

From Figure:

tanΘ =    ………………(i)

Condition for First Minima

d SinΘ = λ

SinΘ =    ……………. (ii)

For small angle Θ, SinΘ ≈ tanΘ

∴ = 

Or, y =    …………(iii)

Which gives the position of first minima from the Centre of the screen.

Width of Central maxima = 2y =2

Diffraction Grating:

Diffraction grating is an optical instrument which is used to determine the wavelength of light. A plane transmission diffraction grating consists of a large number of opaque lines of equal width formed by sharped diamond point on plastic or glass.

Let us consider a plane transmission grating slit width (a) separated by opaque space of wheat b. The quantity a + b is called grating element is given by

d = (a + b)    

where,

N is number of opaque per inch,
N is number of lines per unit length
Theory
Consider light from monochromatic sources that fall on diffraction grating the secondary wavefront at diffraction grating are focused on the screen with the help of lens L.

In the figure point C is the Centre of the screen where the path difference of wavefront is zero. Therefore, a bright pattern is obtained called Central Maxima.
Suppose the secondary wavefront at the slit different at an angle Θ and focused at point on the screen.
The point P will be either maxima and minima depending upon the path differences.

From the figure,

Path difference (x) = ab sinΘ ......(i)

For Maxima:

We have,

x=n λ

ab sinΘ_n = n λ

For Minima:

x=(2n+1) 

ab sinΘ_n=(2n+1)    

Resolving power of optical instrument:

It is defined as the ability of an optical instrument to separate the image of to close point objects at finite distance. Due to these they can be seen distinctly and clearly.

Resolving power of microscope
it is defined as reciprocal of the smallest distance of separation between two point object at which they can be just resolved and shine distinctly through the microscopes
Resolving power of microscope =   = 

Resolving power of Telescope:
It is defined as the reciprocal of the smallest angular separation between two distinct object images that are separated in the telescope.
dΘ=1.22 
Resolving power of Telescope=    =