Diffraction due to a single slit

Single slit diffraction: Definition

Diffraction, which is the bending of light around the margins of an opening or a barrier and it is displayed by all sorts of waves. When light passes through a single slit with a width (a) on the order of the wavelength of the light, we can witness single slit diffraction. The diffraction pattern can be viewed on a screen at a distance L from the slit, where L >> a. The intensity is influenced by the angle at which it is viewed.

Single slit diffraction: formula

For any screen point, we will measure a/2 lengths from its center to determine the angle of the screen. We’ll start with the condition of the black fringes to understand the pattern. Divide the slit into equal-width of a/2 zones. Think about a pair of rays coming from a/2 distances.

For this let us consider a ray coming from the bottom of the slit and another from the middle of the slit, both at a distance of a/2 from one another. Any arbitrary pair of rays at a/2 distance can be taken into account. To create a dark fringe, the path difference must be out of phase by λ /2 (where λ is the wavelength of light).

Therefore,

λ /2 = (a/2) sin θ

Or,  λ  = a sin θ

Since for every ray originating from a point on the slit has a corresponding ray at a distance a/2 that produces destructive interference, destructive interference occurs at the angle θ = sin-1(λ/a). As a result, a dark fringe appears.

The central maximum

On either side of the center, there are two minima, which are separated from each other by a distance which is equal to the width of the central maxima. 

For small θ,

sin θ ≈ θ 

⇒ λ = a sin θ ≈ aθ

⇒ θ = y/D = λ/a

⇒ y = λD/a

The width of the central maximum is simply twice this value

⇒ Width of central maximum = 2λD/a

⇒ Angular width of central maximum = 2θ = 2λ/a

Conditions for diffraction

• Monochromatic light should be used as the primary source of illumination.
• The slit width should be equal to or less than the wavelength of the light that is being reflected.

Types of Diffraction

• Fresnel diffraction: There are fixed distances between the slit and the light source and screen. Incoming waves don’t go in a straight line.
• Fraunhofer diffraction: Using this slit as a reference, we can see that all of the light rays are parallel.

Important facts on diffraction

• There is only one hue, red, at the farthest point in the diffraction pattern of white light. The central maximum is white.
• Any wave can produce diffraction patterns. Electrons, which are subatomic particles, also exhibit patterns that resemble those of light. The discovery of a particle’s wave nature as a result of this observation is regarded as a foundation stone in the development of quantum mechanics.
• Certain crystals have interatomic lengths comparable to an X-ray wavelength. Condensed matter physics investigates the crystal structures of various materials using X-ray diffraction patterns.

Examples and applications of Diffraction in real life-

CD reflecting rainbow colors

Water droplets in the atmosphere split white light into the numerous colors of the rainbow, which is how the rainbow is generated. When seen from a variety of angles, CDs also appear to have the same hues.

Discs are made up of small pits, each with a varied length, that store data. The pits are arranged in a row of equal width and spacing. On the surface of the CD mirror, this creates a diffraction grating.

Holograms

If you’ve ever tried to picture light in a hologram, you’ll know that it’s practically difficult because light travels at an extremely high speed. Your smartphone camera isn’t able to take steady photos when you’re on the go, therefore any photos you take while moving will be blurry. You’ve all heard this before. Light has a speed of 29,97,92,458 m/s, which is what we’re dealing with here. As a result, taking a snapshot of light is practically impossible. But wait, we’ve all seen holograms, which, as we previously established, are steady 3-D photos of light.

This is where the phenomenon of diffraction comes into play. All of us are familiar with the fact that when we toss a stone into a steady stream of water, we produce waves. If you throw two stones at the same time, they will produce two distinct waves that will crash into each other as they go in opposite directions. An interference wave is a type of wave that interferes with another wave. What is this interference wave all about? What happens is that the standing wave is formed when these waves cross one other. This wave can be captured since it can stand stationary.

To generate a holographic image, we employ two separate waves of light to create a standing wave, which can be shot.

Through the shadow of an object

The diffraction of light via an object’s shadow is another real-world example of diffraction. You’ve all seen the effect of a bright light shining behind something. As a result, our object appears as a diffraction shadow. We’ve seen a lot of these kinds of scenarios in movies, particularly horror ones.

Light waves bend along the borders of an item because the object is acting as an obstruction for the lightwave. Our thing appears black because of this.

Spectrometer

A spectrum is present in every wave that travels. When it comes to light waves, spectroscopy uses spectrometers, which is what their name implies. This device aids in the examination of a particular wavelength of light. We can have a thorough understanding of a substance by studying and observing it in this way, and that knowledge can then be applied to the identification of various substances.

Conclusion

Spreading waves are more likely to occur when they have passed through a small opening. If, for example, a door is left open, sound waves that enter the room can be heard even if the geometry of ray propagation suggests that there should be no sound in the room. In the same way, ocean waves that pass through a breakwater’s aperture can reverberate across the bay. Diffraction, which is the bending of a wave around the margins of an opening or a barrier, is displayed by all sorts of waves. Sound and ocean waves are examples of diffraction. Wave diffraction allows waves entering a breakwater opening to propagate throughout the bay.