Class 12 Physics Chapter 10 Wave Optics
In this blog, we will talk about young’s double slit experiment. For this you should be familiar with coherent sources. Coherent sources are two sources emitting waves with same frequency having constant phase difference. To obtain coherent light British Physicist Thomas Young provided an ingenious technique to lock the phases of waves emerging from two sources, such that phase difference between them will always remain constant. For this, he took a cardboard and made a pinhole S in it. Then he took another cardboard and made two closely placed pinholes S1 and S2 in it. Later, he placed two cardboards symmetrically. Light from a bright source is allowed to fall on S and later from S on S1 and S2. The to pinholes then behaves as two coherent sources of light. The two sources S1 and S2behaves as two coherent sources of light. We can say that these are coherent sources because light waves from S1 and S2 are derived from same source. Moreover, the abrupt phase change in the light produced by S will be similar phase change as that of light coming from S1 to S2. this suggest that S1 and S2 produce waves with same frequency and constant phase difference. Thus phases are locked, hence, sources are coherent.
However, if the emergent light from these two sources is allowed to fall on the screen, we get pattern of bright and dark area. It is due to phenomena of interference. Light and dark area are called interference fringes.
The appearance of dark and bright areas are called fringes, which are explained on the basis of interference of light waves. By huygens principle, the source S sends spherical wavefronts. In given diagram, consider, red arcs represent crests,whereas, blue arcs represents troughs. Now, each wavefront reach at S1 and S2 simultaneously. So S1 and S2 becomes sources of secondary wavelets. Moreover, these waves superimpose and undergo interference. Points where crest of one wave fall on other or trough of one wave fall on other, the resultant amplitude of wave is maximum, giving constructive interference. The points where, there is overlap of crest of one wave over trough of other results in formation of destructive interference.
Let S1 and S2 be the two coherent source that produces bright and dark fringes on the screen. d is the distance by which two sources are separated from each other, D be the distance of screen from the sources. Let λ be the wavelength of light. Therefore, nth maxima of constructive interference at nth point is
x = xn= nλD/d
If nth fringe is at maxima then (n+1)th fringe must be at minima. Thus, at n+1 there will be destructive interference. It is given by,
x = xn+1 = (n+1) λD/d
Thus, fringe width can be obtained by :
β = x(n+1) – xn
β = (n+1)λD/d – (n)λD/d
β = λD/d
Keywords: Interference, Constructive interference, Destructive interference, Fringes, Fringe width, Young’s experiment, Double slit experiment