The ratio of the intensity at the center of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the center is

detailed solution

Correct option is A

Resultant intensity at any point on screen is given by  Ir=I1+I2+2I1I2cosϕ .........................................i  where ϕ =  phase difference between the waves  At the center bright fringe ,  Put  I1 = I2 =I     and  ϕ = 0o ⇒Ir=4I.........................................ii  Distance of second point from CB = 14λDd ∴∆x = 14λ ⇒λ2π∆ϕ =  14λ ⇒∆ϕ = π2  To find resultant intensity at second point   Put  I1 = I2 =I     and  ϕ =  π2   in equation (1)  Ir' = 2I .........................................iii   Now take ratio of IrIr' = 4I2I=2