In an interference experiment, the path difference between two coherent waves at point A is λ/3 and at point B is λ/6.

Find the ratio of intensities at points A and B.

Options:

• (1) 3
• (2) 4
• (3) 1/4
• (4) 1/3

For two waves of equal amplitude:

Intensity:

I = 4I₀ cos²(φ/2)

where phase difference:

φ = 2πΔ/λ

At point A:

Δ = λ/3

φ = 2π/3

I_A = 4I₀ cos²(π/3)

= 4I₀(1/2)²

= I₀

At point B:

Δ = λ/6

φ = π/3

I_B = 4I₀ cos²(π/6)

= 4I₀(√3/2)²

= 3I₀

Hence:

I_A : I_B = 1 : 3

= 1/3

Final Answer

Option (4) 1/3