Diffraction: Types, Conditions and Single-Slit Diffraction

Diffraction is the phenomenon that occurs when a wave encounters an obstacle or opening. Diffraction is the interference or bending of waves around corners of an obstacle or through an aperture into the geometrical shadow of the obstacle/aperture.

Key Terms: Diffraction, Conditions for Diffraction, Fraunhofer Diffraction, Fresnel Diffraction, Single Slit Diffraction, Single Slit Diffraction Formula, The Central Maximum

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What is Diffraction?

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Diffraction of light is defined as the slight bending of light waves around the border of a slit or an object. It is the spread of light waves into geometrical shadows. The effect of Diffraction is dependent on the size of the object and takes place when the size of the object is similar to the wavelength of the light. 

Diffraction of Light

The phenomena of diffraction can be observed if the size of the opening is relative to the size of the wavelength of light. The bending will not be noticeable if the opening is much larger than the wavelength of light. The amount of bending is considerable and can be with the naked eye if both are equal or closer in size.

Diffraction occurs with all waves which include water waves, sound waves, and, electromagnetic waves. It occurs when waves of light pass through an opening or slit or even pass by a corner that should be smaller than the light's wavelength or even of the same size. Some examples of diffraction of light are: 

Sun Rays coming from clouds, Bending of light around the corners of windows and doors, etc. 

The below diagram shows how the diffraction of light occurs:

Diffraction of Light

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Conditions for Diffraction

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The conditions for Diffraction are mentioned in the below points:

• The slit width should be similar to the wavelength of incident light.
• The incident light must be monochromatic.

Also Read: 

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Types of Diffraction

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Diffraction is primarily categorized into two types - 

1. Fraunhofer Diffraction
2. Fresnel Diffraction. 

​Fraunhofer Diffraction 

Fraunhofer Diffraction is defined as the source of light and the screen in which the pattern of diffraction is obtained effectively at the limitless or infinite distance from the diffracting system. By using a convex lens, the diffraction pattern is obtained. Fraunhofer Diffraction occurs when the distance is increased and the outgoing diffracted wave becomes straight or horizontal. For eg. Plane Wavefront. The important points for Fraunhofer Diffraction are discussed in the below points: 

• The screen and the source are infinite from each other.
• The incident wavefronts on the diffracting obstacle are horizontal or plane.
• To produce a diffraction pattern, the plane or horizontal wavefront is connected by means of a convex lens.
• Diffraction object gives rise to wavefronts that are also straight or plane.

Fresnel Diffraction 

Fresnel Diffraction occurs due to the size of the obstruction. It is defined as the source of light and the screen in which the pattern of diffraction is obtained effectively at the limited or finite distance from the diffracting system. For eg. spherical or cylindrical wavefronts. The important points for Fresnel Diffraction are discussed in the below points: 

• The screen and the source are near to each other. They are limited or at a finite distance.
• The shapes of Incident wavefronts are spherical or cylindrical.
• The objects left by the wavefronts are also spherical.
• To connect the spherical wavefronts, the convex lens is not needed.

Fresnel Diffraction

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Single Slit Diffraction

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Single Slit Diffraction is that which produces refraction, interference, diffraction, reflection, etc when light travels in the air. The diffraction pattern is formed when light passes through a single slit is different from those formed by diffraction gratings or double slits. Diffraction of light takes place when the light comes in contact with an object.

Observations and Important Notes

• We can observe the diffraction or bending phenomenon of light in a single slit diffraction experiment.
• It produces a unique pattern on the screen known as the Diffraction pattern and also causes light from a coherent source.
• The wavelength on the other side of the opening appears as the wave when light passes through a single slit whose width is comparable to the size of the wavelength.
• When the sources are very small to the size of the wavelength, diffraction is noticeable. For the large or bigger slits, it is unnoticeable. The effect of single-slit diffraction is given in the below diagram.

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Single Slit Diffraction Formula 

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Identify the angular position of any point on the screen by ϑ measured from the slit centre which divides the slit by

 lengths. Observation of the condition of the dark fringes is required to establish the pattern. The slit is divided into equal zones.

This calculation is valid only if D is very large. 

Any number of ray pairings that start from a distance from one another such as the bottom two rays in the diagram can be considered. Any arbitrary pair of rays at a distance can be considered. 

For a dark fringe, the path difference must cause destructive interference; the path difference must be out of phase where λ represents the wavelength.

λ = a sin θ

For a ray emanating from any point in the slit, there exists another ray at a distance that can cause destructive interference.

Thus, at θ = sin−1λa, there is destructive interference as any ray emanating from a point has a counterpart that causes destructive interference. Hence, a dark fringe is obtained.

For the next fringe, the slit is divided into 4 equal parts of a/4 with the same logic applied.

2λ= a sin θ 

Accordingly, for the nth fringe, the slit can be divided into 2n parts and this condition can be used as :

nλ = a sin θ

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The Central Maximum

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The Central Maximum

The maxima between the minima and the width of the central maximum is simply the distance between the 1st order minima from the centre of the screen on both sides of the centre.

The position of the minima given by y and measured from the centre of the screen can be calculated as:

tanθ≈θ≈y/D

For small ϑ,

sin θ≈θ 

λ = a sin θ≈aθ

θ = y/D = λa

y = λDa

Here, the width of the central maximum is twice the value

Width of central maximum = 2λDa

Angular width of central maximum = 2θ = 2λa

Also Read: 

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Things to Remember

• Diffraction of light is defined as the slight bending of light waves around the border of a slit or an object. 
• The phenomena of diffraction can be observed if the size of the opening is relative to the size of the wavelength of light.
• Diffraction occurs with all waves which include water waves, sound waves, electromagnetic waves.
• Diffraction is chiefly of two types - Fraunhofer Diffraction and Fresnel Diffraction. 
• Fraunhofer Diffraction is defined as the source of light and the screen in which the pattern of diffraction is obtained effectively at the limitless or infinite distance from the diffracting system.
• Fresnel Diffraction occurs due to size of the obstruction. It is defined as the source of light and the screen in which the pattern of diffraction is obtained effectively at the limited or finite distance from the diffracting system.
• Single Slit Diffraction is that which produces refraction, interference, diffraction, reflection, etc when light travels in the air.
• The maxima between the minima and the width of the central maximum is simply the distance between the 1st order minima from the centre of the screen on both sides of the centre.

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