The figure shows two point sources of light, A and B. B emits light waves that are +π radians out of phase with the waves from A. A is 3λ from P. B is 5λ from P. (λ is the wavelength.) Find the phase difference between waves arriving at P from A and B. What kind of interference does this situation lead to at P?

 

This problem is not well defined as there is not information about the polarizations of both light sources to make some conclusions about the interference phenomenon.

 

Let we suppose that the light beams of both sources are polarized and have the same polarization directions or were initially generated from the some initial single light source.

Suppose “B emits light waves that are +π radians out of phase with the waves from A” means that Phase of A source have delay on π radians.

 

The distance difference at P, Δd, for the first, A, and the second, B, sources is Δd = 5λ – 3λ = 2λ.

In the phase units this distance difference give the phase shift: Δθ = 2λ * 2π/λ. = 4π radians.

So final phase difference between waves at P from A and B Δθ_f = Δθ – π = 4π – π = 3 π.

 

Coherent light sources gives for this phase difference the destructive interference as wave maximums overlap with wave minimums