Overview: Interference of Light

When two or more waves travel simultaneously in a medium, the resultant displacement at each point of the medium at any instant is equal to the vector sum of the displacements produced by the two waves separately. This principle is called 'principle of superposition'.

The redistribution of light intensity due to the superposition of two light waves is called 'interference of light'.

“Two sources are said to be coherent, if they emit light waves having a sharply defined phase difference that remains constant with time.”

“If the phase difference between two light waves arriving at a point varies with time in a random way, the wave-sources are said to be incoherent.”

“The central white fringe formed when the path difference is zero for all wavelengths is called the zero-order fringe.”

I_{av ​}= \[\frac{I_{\max}+I_{\min}}{2}\]​ = K(a₁²​ + a₂^2​)

• In Young’s double-slit experiment, two narrow slits act as coherent sources, producing an interference pattern of alternate bright and dark fringes on a distant screen.
• Bright fringes are formed by constructive interference when crests meet crests or troughs meet troughs (same phase), resulting in maximum intensity.
• Dark fringes are formed by destructive interference when crests meet troughs (opposite phase), resulting in zero or minimal intensity.
• Fringe width depends on wavelength: red light produces wider fringes than blue light, supporting the wave nature of light.

• Interference occurs when waves from two coherent sources superpose, and the resulting intensity depends on the phase difference between them.
• Resultant intensity at a point is given by
  I = I₁ + I₂ + 2\[\sqrt {I_1 I_2}\] cos ⁡ϕ,
  showing its dependence on phase difference ϕ\phiϕ.
• Constructive interference occurs when the waves meet in phase, i.e., ϕ = 2mπ or path difference x = mλ, resulting in maximum intensity.
• Destructive interference occurs when the waves meet in opposite phase, i.e. ϕ = (2m−1)π or path difference x = (2m − 1)\[\frac {λ}{2}\], giving minimum intensity.
• Alternate bright and dark fringes appear on the screen, producing an interference pattern due to the continuous variation in the path difference.

• A central bright fringe is formed at point O, where the path difference is zero (S1O = S2O).
• Bright fringes occur when path difference = mλ; dark fringes occur when path difference = (2m − 1)λ/2.
• Positions of bright fringes are given by
  x_m = \[\frac {mDλ}{d}\]​
  and dark fringes lie exactly midway between bright fringes.
• Fringe width (β) is the distance between two successive bright or dark fringes and is the same for all fringes:
  β = \[\frac {Dλ}{d}\]
• Fringe width increases with wavelength; hence, red light produces wider fringes than blue light.

• Sources must be coherent — they should maintain a constant phase difference for sustained interference.
• The same frequency (monochromatic light) is required; different frequencies cause intensity fluctuations.
• The principle of superposition must apply for interference to occur.
• The separation between sources should be small to obtain sufficiently wide and visible fringes.
• Screen distance should be set to a large value to increase fringe width and visibility.
• Amplitudes of waves should be equal or nearly equal for maximum contrast between fringes.
• Sources (slits) should be narrow to prevent fringe overlap.
• Monochromatic light is essential to avoid mixing and loss of fringe clarity.