In the Young double-slit arrangement shown in the figure, the incident wavelength is 6000 Å and the screen is 50 cm from the slit plane. At point P, the resultant intensity is equal to the intensity produced by either slit individually. Assuming the two slits contribute equal intensities, what is the path difference between the two interfering waves at P?
Options

Question

In the Young double-slit arrangement shown in the figure, the incident wavelength is 6000 Å and the screen is 50 cm from the slit plane. At point P, the resultant intensity is equal to the intensity produced by either slit individually. Assuming the two slits contribute equal intensities, what is the path difference between the two interfering waves at P?

Options

G1 Physics · Accepted Answer

Let the intensity due to each slit individually be I₀. For two coherent waves of equal intensity, I = 4I₀ cos²(δ ÷ 2), where δ is the phase difference. Given, I = I₀. Therefore, 4I₀ cos²(δ ÷ 2) = I₀, so cos²(δ ÷ 2) = 1 ÷ 4. For the relevant non-zero path difference, δ ÷ 2 = π ÷ 3, so δ = 2π ÷ 3. Phase difference and path difference Δx are related by δ = 2πΔx ÷ λ. Hence, 2π ÷ 3 = 2πΔx ÷ λ, Δx = λ ÷ 3. With λ = 6000 Å, Δx = 2000 Å. Correct option: C.