The figure shows two point sources of light,A and B.B emits light waves that are + $\pi$ radians out of phase with the waves from A.A is 3$\lambda$from P.B is 5$\lambda$ from P.($\lambda$ is the wavelength. )The phase difference between waves arriving at P from A and B is
A)0 rad.
B) $\pi$ rad.
C)2 $\pi$ rad.
D)3 $\pi$ rad.
E)4 $\pi$ rad.

Question

The figure shows two point sources of light,A and B.B emits light waves that are + $\pi$ radians out of phase with the waves from A.A is 3$\lambda$from P.B is 5$\lambda$ from P.($\lambda$ is the wavelength. )The phase difference between waves arriving at P from A and B is 
A)0 rad. 
B) $\pi$ rad. 
C)2 $\pi$ rad. 
D)3 $\pi$ rad. 
E)4 $\pi$ rad.

Quizplus · Accepted Answer

The phase difference between waves arriving at P from A and B can be calculated using the formula:
Δϕ = 2π(Δx/λ) + Δθ
where Δx is the difference in path length from A and B to P, λ is the wavelength, and Δθ is the phase difference between their waves.

In this case, Δx = | AP - BP | = |3λ - 5λ| = 2λ
Δθ = -π (since B is emitting waves that are π radians ahead of A)

Substituting these values in the formula, we get:
Δϕ = 2π(2λ/λ) - π = 3π

Therefore, the phase difference between waves arriving at P from A and B is 3π radians, which is the same as option D).

The Figure Shows Two Point Sources of Light,A and B π\piπ

The Figure Shows Two Point Sources of Light,A and B $\pi$