In a Young's double-slit experiment, each slit individually produces intensity I. Point P lies between the third dark fringe and the third bright fringe on the positive-y side, and the resultant intensity at P is I. What is the phase difference between the two waves at P when reduced to the range from 0 to 2π?
Options

Question

In a Young's double-slit experiment, each slit individually produces intensity I. Point P lies between the third dark fringe and the third bright fringe on the positive-y side, and the resultant intensity at P is I. What is the phase difference between the two waves at P when reduced to the range from 0 to 2π?

Options

G1 Physics · Accepted Answer

For intensity I, I = 4I cos²(φ ÷ 2), so cos²(φ ÷ 2) = 1 ÷ 4. The positional condition gives Δ = 8λ ÷ 3. Therefore the total phase difference is φ(total) = 2πΔ ÷ λ = 16π ÷ 3. Subtract two complete cycles: 16π ÷ 3−12π ÷ 3 = 4π ÷ 3. Thus the reduced phase difference is 4π ÷ 3. Correct option: C.