Skip to main content

Young Double slit experiment



Young in 1801 demonstrated interference phenomenon through double slit experiment
In his experiment ,he divided a single wave front into two and these two slit wave fronts acts as if they emerged from two sources having fixed relationship




when these two waves were allowed to interfere ,they produce a sustained interference pattern
In his original experiment he illuminates a pin hole S using a light source and light diverging from pinhole which contains two sets of pinholes S1 and S2 equidistant from S and very close to one another as shown below in the figure


Two two sets of spherical waves coming out of the pin holes S1 and S2 were coherent and interfered with each other to form a symmetrical pattern of varying intensity on screen XY
This interference pattern disappear when any one of the pinholes S1 or S2 is closed
Young used the superposition principle to explain the interference pattern and by measuring the distance between the fringes he managed to calculate the wavelength of light.

Theory of interference fringes

In young's double slit experiment ,light wave produce interference pattern of alternate bright and dark fringes or interference band
To find the position of fringes, their spacing and intensity at any point P on screen XY .Consider the figure given below



Here S1 or S2 two pin holes of YDS interference experiment and position of maxima and minima can be determined on line XOY parallel to Y-axis and lying on the plane parallel to S,S1 or S2
Consider a point P on XY plane such that CP = x.The nature of interference between two waves reaching point P depends on the path difference S2P-S1P
from figure (6)



for x, d<<< D , S1P+S2P =2D
with negligible error included , path difference would be


And corresponding phase difference between wave is



i) Condition of bright fringes(constructive interference)
If the path difference (S2P-S1P) is even multiple of λ/2,the point P is bright


Equation (21) gives the condition for bright fringes or constructive interference

ii) Condition for dark fringes (destructive interference)

If the path difference is an odd multiple of λ/2,the Point P is dark. So,


Equation (22) gives the condition for dark fringes or destructive interference
From equations (21) and (22) ,we can get position of alternate bright and dark fringes respectively
Distance between two consecutive bright fringes is given by

Thus the distance between two successive dark and bright fringes is same. This distance is known as fringe width and is denoted by β. Thus





Popular posts from this blog

Interference in Wedge Shaped Film (Reflected Rays)

Thin Film Interference A film of thickness from 0.5 to 10  m is a transparent medium of glass, mica, air enclosed between glass, soap film, etc. When the light is made incident on this thin film partial reflection and partial refraction occur from the top surface of the film. The refracted beam travels in the medium and again suffers partial reflection and partial refraction at the bottom surface of the film. In this way several reflected and refracted rays are produces by a single incident ray. As they moves are superimposed on each other and produces interference pattern. Interference in Parallel Film ( Reflected Rays) Consider a thin film of uniform thickness ‘t’ and refractive index   bounded between air. Let us consider monochromatic ray AB is made incident on the film, at B part of ray is reflected (R 1 ) and a part is refracted along BC.At C The beam BC again suffer partial reflection and partial refraction,  the reflected beam CD moves again suffer partial

Lloyd's’ mirror experiment

Lloyd's mirror This is another method for finding the wavelength of light by the division of wavefront. Light from a slit So falls on a silvered surface at a very small grazing angle of incidence as shown in the diagram (Figure 1). A virtual image of So is formed at S1. Interference occurs between the direct beam from So to the observer (0) and the reflected beam The zeroth fringe will be black because of the phase change due to reflection at the surface.  Application An interesting application of this effect may be observed when a helicopter flies above the sea near a radio transmitter. The helicopter will receive two signals: (a) one signal directly from the transmitter and (b) a second signal after reflection from the sea As the helicopter rises the phase difference between the two signals will alter and the helicopter will pass through regions of maxima and minima. Lloyd's mirror Experiment Lloyd’s Mirror is used to produce two-source interference

Thin-Lens Equation:Newtonian Form

In the Newtonian form of the lens equation, the distances from the focal length points to the object and image are used rather than the distances from the lens. Newton used the "extrafocal distances" xo and xi in his formulation of the thin lens equation. It is an equivalent treatment, but the Gaussian form will be used in this resource.