2019:
The answer is d = √2D
The intensity at the center of the screen is given by:
I = I1 + I2 + 2√I1I2cosθ
where I1 and I2 are the intensities of the two sources and θ is the phase difference between them.
In this case, the two sources are coherent, so θ = 0 and the intensity at the center of the screen is:
I = 4I
The distance between the two sources is d, and the distance from the sources to the screen is D. The phase difference between the two sources at a point on the screen a distance x from the center is given by:
θ = 2πdx/λD
At the center of the screen, x = 0, so θ = 0.
If the distance between the two sources is decreased to half its original value, d = √2D, then the phase difference at the center of the screen will be:
θ = π/2
The intensity at the center of the screen will then be:
I = I1 + I2 + 2
