Wave Nature of Light with Young’s Double-Slit Experiment
1. Wave
A wave is a disturbance that propagates through space or a medium, transferring energy from one point to another without transporting matter.
Example: When we make a sharp needle vibrate in a calm pool of water, a circular pattern spreads out from the point of impact. The vibrating needle creates a disturbance that propagates outwards. In this propagation, the water molecules do not move; instead, they move in nearly circular orbits about an equilibrium position. Once the disturbance has passed a certain region, every drop of water is left at its original position.
Fig. 1. Ray diagram of Young's Double Slit interference.
2. Nature of Light
Light exhibits wave-particle duality, meaning it behaves both as a wave and as a particle under different experimental conditions.
(a) Particle Nature of Light
A particle is a discrete portion of matter. We refer to light particles as photons because of their particle nature. In the 17th century, Sir Isaac Newton proposed the corpuscular theory of light, suggesting that light consists of a stream of particles. He supported this idea because when he used a prism to split sunlight into different colours, the periphery of the shadows created was extremely sharp and clear.
(b) Wave Nature of Light
A wave is a periodic disturbance that propagates through space or a medium, transferring energy without transporting matter. The wave nature of light states that light is a particular kind of electromagnetic wave. Humans can detect only a small portion of the electromagnetic spectrum, known as visible light. The first illustration of the wave nature of light was made using experiments on diffraction and interference.
3. Interference
When two coherent light waves, i.e., have a constant phase difference superpose on each other, there is a modification in the intensity of light in the region of superposition. This variation in intensity is the interference phenomenon.
Interference produces two types of fringes:
(a) Constructive Interference (Bright Fringes)
Constructive interference occurs where the lines (representing peaks) cross over each other — in other words, when two waves are in phase.
Fig. 2. Schematic diagram of constructive interference.
Condition: d sinθ = nλ (n = 0, 1, 2, …) …(1)
Position of n-th bright fringe on screen: yₙ = nλD / d (n = 0, 1, 2, …) …(2)
where:
- θ = diffraction angle (rad)
- d = slit spacing (m)
- λ = wavelength of light (m)
- D = distance from slits to screen (m)
- n = order of the fringe
- When n = 0, θ = 0 → central bright fringe
(b) Destructive Interference (Dark Fringes)
Destructive interference occurs where two waves are completely out of phase — when two waves are out of phase by 180° or π.
Fig. 3. Schematic diagram of destructive interference.
Condition: d sinθ = (n + ½)λ (n = 0, 1, 2, …) …(3)
Position of n-th dark fringe on screen: yₙ = (n + ½)λD / d (n = 0, 1, 2, …) …(4)
where:
- θ = diffraction angle (rad)
- d = slit spacing (m)
- λ = wavelength of light (m)
- D = distance from slits to screen (m)
4. Interference Fringes
When two coherent light waves interfere, alternate dark and bright bands are observed on the screen. These are called interference fringes.
5. Young's Double Slit Experiment (YDSE)
In this experiment two coherent sources are created from one source by division of wavefront. When light passes through a single pinhole S and then through two closely spaced pinholes S₁ and S₂ separated by distance d, two spherical coherent waves emerge, producing alternating bright and dark fringes on a screen.
Key parameters:
- d : distance between the two slits
- D : distance from the slits to the screen
- S₁ and S₂ must be coherent sources
Coherent Sources: Two or more sources are said to be coherent if the waves originating from them have the same frequency (or wavelength) and bear a constant phase difference with time.
6. Methods of Obtaining Coherent Sources
Division of Wavefront
- Young's double-slit - Slits S1 and S2 act as coherent sources.
- Lloyd's mirror – Slit S and its virtual image S′ act as coherent sources.
- Fresnel's biprism – Two coherent sources formed by refraction through a biprism.
Division of Amplitude
- Thin films – Coherence is obtained by partial reflection and transmission of light.
7. Fringe Width
Fringe width (β) is defined as the distance between two consecutive dark or bright fringes.
Formula: β = λD / d …(5)
where:
- β = fringe width (m)
- λ = wavelength of wave (nm)
- d = distance between the slits (m)
- D = distance from slits to screen (m)
The expression for fringe width is the same for bright and dark fringes.