Interference of Young’s double-slit experiment

Introduction

Young successfully carried out an experiment to determine the wavelength of light in 1801. Young’s problem was that the normal light sources of the day (candles, lanterns, etc.) couldn’t be used as coherent light sources. Young’s solution involves letting sunlight into the room through a pinhole in a window shutter. The pinhole beam was directed horizontally across the room using a mirror. Young utilised a thin paper card to divide the single pinhole beam into two beams, with part of the beam travelling through the left side of the card and part of the beam travelling through the right side of the card.

Interference

Interference of Light Waves is described as a change in the distribution of light energy caused by the superposition of two or more waves. These sources should produce continuous waves with the same wavelength and time period. These sources should be as near as possible to one another. The sources that generate light waves must be coherent. The interference pattern is visible and stable if the waves are coherent. The pattern is not apparent if the waves are incoherent.

There are two types of Interference

• Constructive

When the peak of one wave collides with the crest of another, the resulting amplitude is maximum. The condition in which the resulting amplitude is greatest is referred to as constructive interference.

• Destructive

When the peak of one wave collides with the trough of another, the resulting amplitude is the smallest. Destructive Interference refers to the situation in which the resulting amplitude is the smallest.

Young’s Double-Slit Experiment

The existence of overlapping waves is firmly shown by interference effects. Thomas Young proposed that light is a wave subject to the superposition principle; his greatest experimental success was to establish light’s constructive and destructive interference. A laser illuminates two parallel slits in an otherwise opaque surface in a contemporary version of Young’s experiment, which differs only in the source of light. A faraway screen displays the light travelling through the two apertures. When the slit widths are much higher than the wavelength of the light, the geometrical optics laws apply—the light casts two shadows and illuminates two zones on the screen.

The ratio of the wavelength of the light λ to the spacing of the slits, d, is a crucial parameter in the double-slit geometry. If λ/d is significantly less than one, the spacing between consecutive interference fringes will be short, and the interference effects may be indistinguishable. Young was able to separate the interference fringes by using narrowly spaced slits. In this technique, he calculated the wavelengths of visible light colours.

Formula 

Young’s Double Slit Experiment Derivation

If a glass slab with refractive index μ and thickness t is placed on one of the routes of interfering waves, the optical length of this path becomes μ instead of t, rising by (t-1)μ.

This results in a path difference, which is given by,

 Δx = μt – t = (μ-1)t   

This route variation is caused by the glass slab.

If the present location of the fringe is y =D/d (Δx), the new position is y’ = D/d(Δx + (μ-1)t).

Fringe lateral shift:

 y₀ = y’ – y

 y₀  = D/d(μ-1)t

As an example, fringe width, w = D/dλ 

We get,

 y₀ = β/λ (μ-1)t

Conclusion 

Young utilised a thin paper card to divide the single pinhole beam into two beams, with part of the beam travelling through the left side of the card and part of the beam travelling through the right side of the card. Interference of Light Waves is described as a change in the distribution of light energy caused by the superposition of two or more waves. When the peak of one wave collides with the trough of another, the resulting amplitude is the smallest is known as destructive interference. The existence of overlapping waves is firmly shown by interference effects. The ratio of the wavelength of the light to the spacing of the slits, d, is a crucial parameter in the double-slit geometry.