Engineering Physics: Notes of Interference and Diffraction | Part 2

 1st Semester Notes for B.tech

Engineering Physics: Notes of Interference and Diffraction | Part 2

Here we will discuss Engineering Physics notes. In which this site will provide you all chapter notes for 1st Semester and if you want all this in pdf then comment below. 

In this part, we will discuss Diffraction.

Diffraction

The phenomenon of bending of light around the sharp corner and spreading light is known as Diffraction.

Light bends through a sharp surface when it bumps on the edge and spreads light into a brighter and shadowed region.

S: Source of monochromatic light

MN: Screen which shows diffraction of light

There are two types of diffraction based on their location:

1. Fresnel Diffraction
2. Fraunhofer Diffraction

Fresnel Diffraction	Fraunhofer Diffraction
Source and Screen both are at a finite distance from the narrow slit	Source and Screen both are at a infinite distance from the narrow slit
The lens isn't used	Lenses are used
Incident Wavefronts are Spherical	Incident Wavefronts are plane

• Fresnel Diffraction

• Fraunhofer Diffraction due to a single slit

S: monochromatic light source

L: Lens of Focal length f1 

L1: Lens of Focal length f2 

MN: Narrow Slit

AB: Screen

    Amplitude= Aθ = KaSinα/α

    Intensity (I) at P = IoSin²β/β²

    Io is the maximum intensity and β= πbsinθ/λ

• Condition for minima

for minima, I=0

    IoSin²β/β²= 0

    Sinβ=0

Therefore, β=nπ    -------(n=0.1,2,3.......)

if β→0

    lim Sinβ/β  =1

    β→0

    Principle maxima are I=Io 

        β=πbsinθ/λ 

• Condition for maxima

In this case, dI/dβ=0

    2IoSinβ(βCosβ-Sinβ)=0

    tanβ=β

This equation is known as the Transcendental equation

Difference Between Interference and diffraction of light:

Interference	Diffraction
Two different wavefronts originate through the same monochromatic source	due to bumping with the edge of an obstacle, it comes from different part of the same wavefronts
the fringe of  interference have the same width	the fringe of  diffraction doesn't  have the same width
The intensity distribution of bright fringe is the same	The intensity distribution of fringes is not the same

Diffraction Grating

Distance between two consecutive slits is equal and parallel in a large number of a glass plate is known as a diffraction grating. It has approx. 400 to 5000 lines/centimeter.

Elements of grating: The grating element is the distance between two adjacent slits. It is denoted by 'd'.

    d= L/N

where L is the length of the grating

           N is the number of adjacent lines

SI unit: meter(m)        Dimensional Formula: [L]

• Parallel rays of two consecutive slits differ in the path by lambda(λ) and the distance between two rays is ab

            ab=λ 

From the figure,    Sinθ=ab/d=λ /d

Types of diffraction grating:

1. Ruled grating
2. Holographic grating

Images formed due to diffraction grating:

• Zeroth order

when θ=0, along normal then the path difference between two consecutive rays will be zero. The bright image form is known as the zero-order image form diffraction grating.

    Therefore, dSinθ=λ=0

• First-order

When θ increases then the path difference between two consecutive rays(λ) will have a positive value. The bright image form is known as the first-order image form diffraction grating.

    Therefore, dSinθ=λ=positive value

• By increasing θ we will get 2nd, 3rd....Nth order.

Notes: (i) if d and θ will be same and λ increases then there will increase in orders

            (ii) if d and λ will be the same and θ increases then images will be of different colour forms.

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