The principle of superposition is used to understand the phenomenon of interference of…

The principle of superposition is used to understand the phenomenon of interference of light waves. The principle states that at a particular point, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each wave. Light waves from two coherent sources produce interference pattern. Thomas Young devised a way to obtain two coherent sources using two identical pinholes (S₁ and S₂) illuminated by a single monochromatic pinhole source S. Using these sources in his experiment known as Young's double slit experiment, Young studied the interference pattern. The pattern consists of alternate bright and dark fringes. The distance between two successive bright or dark finges depends on the distance between S₁ and S₂, the distance of the screen from the plane of S₁ S₂ and the wavelength of light used.

Consider the following waves:

1. y₁ = a sin \(\omega\) t
2. y₂ = a sin 2 \(\omega\) t
3. y₃ = a sin (2 \(\omega\) t + \(\phi\) )
4. y₄ = a sin (4 \(\omega\) t + \(\frac{\pi}{2}\) )

Which pair of the waves coming from two sources S₁ and S₂ will produce interference?