In a two-wave interference experiment, the path difference between the coherent waves at point A is λ/3, while at point B it is λ/6. Using the equal-intensity condition employed in the given solution, what is the ratio of the resultant intensities $I_{A}$ / $I_{B}$ ?
Options

Question

In a two-wave interference experiment, the path difference between the coherent waves at point A is λ/3, while at point B it is λ/6. Using the equal-intensity condition employed in the given solution, what is the ratio of the resultant intensities $I_{A}$ / $I_{B}$ ?

Options

G1 Physics · Accepted Answer

For two coherent waves of equal individual intensity I, the resultant intensity is I(resultant) = 2I[1+cosδ], where δ = 2π(Δx ÷ λ). At point A: δ(A) = 2π(1 ÷ 3) = 2π ÷ 3. Therefore, I(A) = 2I[1+cos(2π ÷ 3)] = 2I(1-1 ÷ 2) = I. At point B: δ(B) = 2π(1 ÷ 6) = π ÷ 3. Thus, I(B) = 2I[1+cos(π ÷ 3)] = 2I(1+1 ÷ 2) = 3I. Hence, I(A) ÷ I(B) = 1 ÷ 3. Correct option: C.

In a two-wave interference experiment, the path difference between the coherent waves at point A is λ/3, while at point B it is λ/6. Using the equal-intensity condition employed in the given solution, what is the ratio of the resultant intensities I A I_{A} I A ​ / I B I_{B} I B ​ ?

In a two-wave interference experiment, the path difference between the coherent waves at point A is λ/3, while at point B it is λ/6. Using the equal-intensity condition employed in the given solution, what is the ratio of the resultant intensities I A I_{A} I A / I B I_{B} I B ?