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# Diffraction

## Diffraction

Diffraction is the bending of light waves when it passes around the edge of the object. The amount of bending of light depends on exact wavelength of light and the size of opening. The diffraction effect are more visible and detectable if the size of the object is small. If the wavelength of the light wave is greater, the amount of diffraction is also higher.

For Example, in the atmosphere diffracted light is bent around atmospheric particles which are tiny water droplets found in the clouds. A laser will show better effects of diffraction over long distances which may be due to the coherence of laser light. Diffraction occurs with waves like water waves, sound waves-rays and radio waves. As we have interference pattern of dark and bright fringes, there is diffraction pattern which produces dark and bright points on the screen. It contains a bright fringe, dark fringe and central maxima. Diffraction

## Types of Diffraction

There are two types of diffraction.

### Fresnel Diffraction

If the source or the screen or both of them are at finite distance from the obstacle, the diffraction which takes place is called Fresnel Diffraction. It is also known as Near- Field Diffraction. Fresnel diffraction occurs on spherical surfaces. It occurs with cylindrical wavefronts. Diffraction at narrow wire and straight edge are examples for Fresnel diffraction.

### Fraunhoffer diffraction

If the source or the screen or both of them are at infinite distance from the obstacle, the diffraction which takes place is called Fraunhoffer Diffraction. It is otherwise known as Far-Field Diffraction and occurs on flat surfaces. It occurs with plane wavefronts. Diffraction at double slit, single slit are examples for fraunhoffer diffraction.

## Single Slit Experiment

As we consider double slit in Young’s experiment for interference, here it is replaced by single narrow slit. We use a monochromatic coherent source here.  A coherent source emits light with constant phase difference. When light falls on the slit, it deviates through the slit. Thus diffraction occurs. The light then falls on the screen which is placed at a long distance from the slit. It then produces a pattern of alternate bright and dark images of the slit. Also a broad pattern with a central bright region is also seen. The intensity becomes weaker when moving away from the center. The diffraction process can be explained by considering light in the form of electromagnetic wave. The diffraction pattern consists of the central maximum and a sequence of secondary maxim and minima. The pattern will be similar to an interference pattern. Single slit diffraction

Consider the path of five rays which emerges from different portion of the slit. Here the Huygens’s principle comes into picture. When the light wave travels through the slit each and every point on the slit act as a source of secondary waves. The wave one is from the bottom of the slit and wave three is from the center of the slit. The difference in path is considered as (a sin θ) /2. Here ‘a’ is considered as the width of the slit and θ is the angle each rays makes with the horizontal. Single slit experiment

The path difference between the rays two and four is also (a sin θ) /2. If the path difference is  which is half the wavelength, then the two waves are 180° out of phase and interfere destructively and thus cancel each other. So the waves from the upper half of the slit is 180° out of phase with the light waves from the lower half of the slit when

(a sin θ) /2 = is λ/2.

Divide the slit into 2n portions. The condition for destructive interference is met at angles θ on the screen which is above and below the center of the pattern and is Sinθ = n λ/α, m being an integer 1, 2, 3…. This is the condition for darks. a sin θ = λ. This is the condition for first dark in the diffraction pattern.

Central bright is decided by the position of first darks.

The condition for the maxima or the bright ones are a sin θ = (n + 1/2) n = 1, 2, 3… For the first bright, n = 1

a sin θ = 3λ/2. The diffraction pattern is negligible if a>>λ.

## Optical Instruments and Diffraction

Diffraction of light plays an important role in controlling the resolving power of eyes and optical instruments like telescopes, microscopes, binoculars etc. The resolving power of the instruments is its capability to produce separate and clear images of two closer points. This is often resolved by the quality of the lenses and the mirrors which are used in the instruments. The objective lens of those instruments behaves like a circular aperture. These circular aperture produces diffraction patterns and due to this, the beam which is to be focused to a point gets focused to a spot of restricted area. It produces a brighter disc known as Airy disc which is surrounded by alternate bright and dark rings.

The mathematical expression for this diffraction pattern is Sin θ = 1.22 λ/d, where θ is the angular position, λ is the wavelength of the incident light, d is the diameter of the aperture and 1.22 is the constant. To get a clear and perfect image, the point sources should be imaged in such a way that their images are meant to be very far such that the diffraction patterns do not overlap. For a good resolution we need a high refractive index medium. Oil immersion microscopes use oil to have greater refractive index. We can also get a good resolution by decreasing the wavelength using X-rays and gamma rays.

## Diffraction grating

Diffraction grating is the tool used separate light of different wavelengths with high resolution. They are used in many areas of physics and astronomy. It is used for measuring atomic spectra in laboratory instruments and telescopes. They use the principle of both constructive and destructive interference of light waves to separate different wavelengths which is based on the wave behavior of light. Diffraction grating

The diffraction grating comprises large number of closely spaced and parallel slits. It can be either transmissive or reflective. When light wave transmit or reflects off the grating, the grooves causes the light waves to diffract and separating light into different wavelengths. The diffraction grating equation is a Sin θ = nλ, where a is the grating spacing, θ is the angle of incident light, n is the diffraction order and λ is the wavelength of light.

Diffraction gratings are involved in CD players. Holographic diffraction grating, reflective blazed holographic diffraction grating, reflective ruled diffraction grating are the different types of grating. We can make diffraction grating by finely marked lines on the reflecting surface of CD. Interference peaks will be sharper by increasing the number of slits in the grating.

Comparison between Interference and Diffraction

 Interference Diffraction Interference occurs due to the superposition of wave from two coherent sources. Diffraction occurs due to the superposition of wavelets from different parts of the wavefront. It requires only a single coherent source. Interference pattern has a number of equally spaced darks and bright bands. Diffraction pattern has a central bright maximum All fringes will be of same intensity. Intensity is not the same for all fringes. It lowers when it goes to successive maxima which is away from the center. Intensity of all minima can be zero. Intensity of all minima cannot be zero. Path difference for nth maxima ∆ = n λ Path difference for nth secondary maxima ∆ = (n + 1/2) λ Path difference for nth minima ∆ = (n – 1/2) λ Path difference for nth minima ∆ = n λ

In the case of both interference and diffraction, there is no gain or loss of energy. They both support the wave theory of light. Sir Isaac Newton’s corpuscular theory could not explain the interference and diffraction phenomena.

## Summary

• Diffraction is the redistribution of waves after passing through an obstacle. Diffraction can be divided into two - Fresnel Diffraction and Fraunhoffer Diffraction.
• In Fresnel diffraction the source and the screen will be at finite distance from the object. In Fraunhoffer diffraction, the source and the screen will be at infinite distance from the object.
• In Single slit experiment Sin θ = n λ/α, m being an integer 1, 2, 3… is the condition for darks. The condition for the maxima or the bright ones are a sin θ = (n + 1/2) λ, n = 1, 2, 3…
• Diffraction grating is used to separate light of different wavelengths and high resolution.
• Both Interference and diffraction support the wave theory of light.

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