Intensity of wave ∴ I = a 2 + b 2 + 2ab cos φ = I 1 + I 2 + 2 √I 1 I 2 cos φ
where I 1 and I 2 are intensities of two waves . ∴ I 1 / I 2 = a 2 / b 2 = ω 1 / ω 2
Where ω 1 and ω 2 are width of slits . Energy remains conserved during interference . Interference fringe width β = Dλ / d
where , D = distance of screen from slits , λ = wavelength of light and d = distance between two slits .
Distance of nth bright fringe from central fringe x n = nDλ / d Distance of nth dark fringe from central fringe x ’ n = ( 2n – 1 ) Dλ / 2d
Coherent Sources of Light
The sources of light emitting light of same wavelength , same frequency having a zero or constant phase difference are called coherent sources of light .
When a transparent sheet of refractive index μ and of thickness t is introduced in one of the path of interfering waves , then fringe pattern shifts in that direction by a distance Y
Y = D / d ( μ – 1 ) t = β / λ ( μ – 1 ) t where , β = fringe width .