The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is
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Total intensity at any point is given by `I = kR^(2) = k (a^(2) + b^(2) + 2 ab cos phi)` when `b = a, I = k (a^(2) + a^(2) + 2 a^(2) cos phi)` `= 2 ka^(2)(1 + cos phi)` At the centre of a bright fringe, `phi = 0^(@)` `:. I_(1) = 2 ka^(2)(1 + cos 0^(@)) = 4 ka^(2)` Distance between two fringes `= beta`, which is proportional to wavelength `(lambda)` Now `(lambda)/(4)` corresponds to a phase diff. `= (2pi)/(4) = (pi)/(2)` `:. I_(2) = 2 ka^(2) (1 + cos pi//2) = 2 ka^(2)` `:. (I_(1))/(I_(2)) = (4 ka^(2))/(2 ka^(2)) = (2)/(1)`
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