Optics Interference With Coherent & Incoherent Waves

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/λ

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 = D/2, 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 + I3