Young’s Double Hole Experiment and Equation

The behaviour of light, as a rule, depicts the conduct of apparent, bright, and infrared light. The experiment is demonstrated by Young’s double-hole experiment, or the modern, two-hole experiment, or the double-hole experiment, that both light and matter exhibit properties of both wave and particle. Apart from this, the experiment also shows the probabilistic nature of quantum mechanical phenomena. Young’s double-hole experiment was originally done by Thomas Young in 1801.

Many scientific theories fail in front of this experiment, and it has also shaken Quantum Mechanics. Let us know what Young’s Double hole Experiment challenged the existence of modern science.

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In this experiment, two parallel thin holes were made in a metal plate. This hole had a light source on one side and a curtain or board on the other. Patterns are formed on the screen by the passage of light through the holes. The laws of light are studied by analysing these patterns. This experiment was first done by the 18th-century scientist Thomas Young, hence this experiment is called Thomas Young’s Double hole Experiment.

Let’s take a point light source, a circular wavefront is being emitted from it. A rectangular cardboard M is placed at a distance b from a point type source S.

Two holes, S1 and S2, are made at the same distance from point O of the cardboard. The distance between them is d. The curtain is kept at a distance D from the rectangular cardboard M. When a point (light) is incident from a source (S) on types S1 and S2, then S1 and S2 behave like a two-phase relationship of light sources, from which the light is transmitted forward in the form of secondary waveforms. These secondary wavelets are transmitted between the rectangular cardboard, M, and the screen, N, and after transmission, these secondary wavelets are superimposed on the screen, resulting in an interference pattern.

In Young’s double hole experiment, bright and dark fringes are obtained in an alternate sequence on the interference pattern screen.

The distance between two consecutive bright fringes or two consecutive non-luminous fringes is the same.

Fringe Width (B): The distance between two consecutive bright fringes or two consecutive non-luminous fringes is called fringe width. It is denoted by B (beta). Its unit is metre (m).

Let the distance between the two holes A and B be ‘d’, and the distance between the screen from these points is D as shown in the figure and be the wavelength λ of the light emerging from the holes.

A light wave travelling from points A and B meets the screen P. Here, they can be in the same phase as well as in the opposite phase, depending on the distance travelled by them. The distance of this point P from the central fringe is x.

So the path difference between the interference waves δ = xd/D

Here theta is considered small.

Position of bright fringe

According to the principle of interference, the condition for path difference of a complementary interference = nλ

 xd/D = nλ

Here n = 1,2,3, ……… This is the order of the bright fringe.

 Thus, for nth bright fringe, x = (D/d) nλ

Position of the dark fringe 

According to the law of interference, the path difference of a malnourished wave interference = (2n-1)λ/2

Here n = 1,2,3, ……… This is the order of the dark fringes.

Thus, the case for nth dark fringe x = (D/d) [(2n – 1)λ/2]

Width of fringe

The distance between two consecutive bright and non-luminous fringes is called the width of the fringe.

Fringe width β = Dλ/d

Constructive and Destructive Interference

For constructional interference, the method difference must be a significant frequency of the wavelength. 

So for a bright fringe to be at ‘y’,

nλ = y d/D

Or, y = nλD/d

Where n = ±0,1,2,3…..

The 0th fringe represents the bright middle fringe.

Similarly, the expression of the black fringe in the Young double-hole test can be obtained by setting the method difference by:

Δl = (2n+1)λ/2

This simplifies to

(2n+1)λ/2 = y d/D

y = (2n+1)λD/2d

In 1801, Thomas Young demonstrated the wave nature of light with his double-slit experiment. Monochromatic light is shone through two tiny slits in this experiment. After travelling through each slit, the waves superimpose on a distant screen, resulting in alternative brilliant and dark fringes. The intensity and fringe width of all the bright fringes are the same.

Monochromatic light is transmitted through a single slit of limited width in a single slit experiment, and an identical pattern appears on the screen. The width and intensity of the single-slit diffraction pattern decrease as we travel away from the central maximum, unlike the double-slit diffraction pattern.

Some results came out in it which were as follows –

1. Some bright bands are found on the curtain which is kept, which are called bright fringes and some black strips are found, which are called dark fringes. And these bright fringes and dark fringes are obtained in alternate order and when bright fringes and non-dark fringes are obtained in an alternate sequence, then the group of these fringes is called an interference pattern.

2 . The intensity of all the bright stripes, i.e. the bright fringes obtained on the screen and the intensity of all the black strips, i.e. the dark fringes, remains the same, out of which the intensity of the bright fringes is maximum, and the intensity of the dark fringes is minimum or almost zero.

4. Simultaneously, it was also seen that the distance between any two bright or bright fringes received on the screen or any two black or dark fringes remains the same, and this distance is also called the width of the fringe.
5. All bright and dark fringes have the same width.

Thus these were some of the results which were obtained on the basis of Young’s double hole experiment.

Conclusion

The mystery of not understanding light raises many big questions on science. For example, are the basic principles of our science wrong? Is there some supreme being who wants to keep its hidden secrets hidden? Is every particle controlled by some supreme being? Perhaps in the future, the reason for this may be known exactly, but at the moment, it will not be wrong to understand the result of the Double hole Experiment.