Coherent source
Two sources are said to be coherent if they emit a light wave of the same wavelength, same amplitude and they are in the same phase with each other having a constant phase difference
It is not possible two independent sources are coherent but experimentally two virtual sources come from a single source that acts as a coherent source
Interference
When two waves of the same frequency having constant, phase difference traveling in the same direction will meet, they produce a resultant wave by superposition principle. Thus the modification in the intensity of light due to the superposition of two or more waves is called interference.
Types of interference
1. Constructive interference
If two waves having the same frequency and same phase overlap with each other, the amplitude of the resultant wave means a resultant wave of more intensity will form. Such interference is called constructive interference.
Fig: Constructive Interference
∴path difference = nλ
Destructive Interference
If two waves of the same frequency and same amplitude travel in the same direction with opposite phases to each other then a resultant wave of zero amplitude is formed. Such interference is called destructive interference in which the intensity of light will be minimum.
Fig: Destructive Interference
∴path difference = (n + 1/2) λ
Condition to produce interference
1) Two-Source of light must be coherent
2) Light source used must be monochromatic
3) Two sources of light must be closed to each other
4) The distance between the coherent source of the light and the screen should be large.
5) Coherent source of light must be narrow
6) Coherent source of light must emit waves continuously.
Young’s double-slit experiment
Fig:-Young double-slit experiment
Let ‘s’ be the monochromatic source of light having wavelength ‘λ’. Also, let S1 and S2 be the two-slit which are equal distance from source ‘s’ act as coherent sources suppose ‘D’ be the distance between source as know at which path
Also, suppose ‘C’ be the center of the screen at which the path difference is zero. Hence at point ‘C’ maximum intensity is observed. Also, let ‘P’ be any point at distance ‘I’ from ‘C’.
Also,
If ‘P’ is very close to C
S2P ≈ S1P ≈ D
Bright Frings
The point 'p' has a maximum,
Which gives the distance of n^th bright fringe from center
Which is the width of bright fringes
Dark fringes
The point 'P' has maximum
Which gives the distance of n^th dark fringe from center
For n = 0
For n = 1,
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