If E is the amplitude of the electric field of the waves starting from the slits in a double slit experiment and is the phase difference between the waves reaching a point on the screen, the ratio of the amplitude of the resultant electric field at that point on the screen to the amplitude at one of the slits is

Step-by-step solution

Let the electric field of the waves from the two slits be E₁ = E ( t) and E₂ = E ( t + ) , where E is the amplitude of each wave and is the phase difference. The resultant electric field E_R is given by the superposition principle: E_R = E₁ + E₂ = E [ ( t) + ( t + )] . Using the trigonometric identity A + B = 2 ( A+B 2 ) ( A-B 2 ) , we get: E_R = E 2 ( t + 2 ) ( 2 ) . The amplitude of the resultant electric field is the coefficient of the oscillating term, which is 2E ( 2 ) . The ratio of the resultant amplitude to