Q. In young’s double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength λ . In another experiment with the same arrangement the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is I1 and in the second case I2, then the ratio I_{1}/I_{2} is

(a) 4

(b) 2

(c) 1

(d) 0.5

Ans: B

Sol: Let I_{A} = I_{B} = I

At the mid Point of screen Δx = 0 ; φ = 0

*For coherent sources,*

$ \displaystyle I_1 = (\sqrt I_A + \sqrt I_B)^2 $

$ \displaystyle = (\sqrt I + \sqrt I)^2 = 4 I $

*For incoherent sources,*

I_{2} = I_{A} + I_{B}

I_{2} = 2 I

$ \displaystyle \frac{I_1}{I_2} = \frac{4I}{2I} = 2 $