Circuit Theory and Principle for Wheatstone Bridge

Young’s double-slit experiment was used to understand the wave theory of light. The wave theory of light states that a ray of light experiences a change in its path while moving from one medium to another. This theory was put forward by Sir Huygens and is crucial for understanding wave optics. Young’s double-slit experiment proved that light could act both as a particle and a wave at the same time. Dark and bright fringes are formed in the course of this experiment and have a specific fringe width. 

Young’s double hole experiment:

In 1801, Thomas Young tried proving the fact of light being a particle or a wave wrong by performing the double hole or the double-slit experiment. He used two coherent sources of light that were separated by a small distance. The wavelength of light is kept of a slightly greater order than the magnitude of the wavelength of light. 

How was the experiment carried out?

Young placed a photodetector, also called a screen, at a considerably large distance from the slits. The distance between them is denoted by ‘D’. He used diffracted light from a single source in this experiment. The waves travel a distance of a1 and a2 and create a path difference of ∆I at that point. For the distance D, the θ angle is quite less due to its large distance from the slits or the holes. 

This experiment was significant in the history of physics. It proved that light could behave both as a particle and wave simultaneously and prepared a solid base for wave optics. 

The Derivation of Young’s double hole experiment:

Consider a monochromatic light source in nature, denoted by ‘S’. S is placed at an equal distance from both the slits, s1, and s2. They both behave as coherent sources of light as they are both derived from S. The light falls on the photodetector screen after passing through the slits. The interference pattern required can be formed only when both the slits (s1 and s2) are open, and their way is not blocked by any object. 

Let X be a point on the screen where the light rays have to meet after passing through the slits or the holes. The ‘d’ and ‘D’ are kept constant, the distance between the two slits and the distance between the two slits and the screen. Still, they travel different distances to reach point P on the screen, showing that there is a path difference. There can be two conditions of approximations, namely-

D > > d: Since D > > d (The two light rays are assumed to be parallel to each other)

d/λ >> 1, λ is in the order of a few micrometres, and d is in the order of a few millimetres. (for visible light)

sin θ = tan θ  ≈  θ= λ/d Type equation here.

This is because the angle is small. 

The path difference thus can be written as Δz = λ/d. 

This path difference creates a difference between the colours of the fringes developed on the screen. Thus, some of them are dark fringes, and some are light. 

Fringe width and types of fringes:

Distance between two adjacent fringes (dark fringes and light fringes) is called fringe width. 

β = λD/d

The wavelength of the fringe width decreases ‘μ’ times when it is immersed in liquid. 

Bright fringes-

The bright fringes are formed due to constructive interference and have positions of maximum intensity. 

For the formation of bright fringe at P,

The path difference would be = Δz = nλ (n = 0, ±1, ±2….)

We can write that xn = nλD/d

If the distance of the nth fringe from the centre is xn = nλD/d, then the distance of the n-1th fringe would be x(n-1)= (n -1)λD/d

Dark fringes-

They are formed by destructive interference and have positions of minimum intensity.

For the formation of dark fringes at the point P,

The path difference would be Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, .  . .)

The distance for the nth fringe from the centre can be given as, xn = (2n+1)λD/2d, and so go on.

 Conclusion

Young’s double-slit experiment involved a two-slit system that acted as the two coherent monochromatic light sources. This experiment has successfully proven the fact that light can act as a particle as well as a wave at the same time. This leads to the formation of two kinds of fringes at the Point of the intersection at the screen where the light rays fall. These are the dark fringes and the bright fringes. If the interference is positive, the fringe width stays the same throughout. The fringe width is independent of the order of the fringe. Young’s double-slit experiment was crucial for the understanding of wave optics.