In a Young's double-slit experiment, each slit individually produces intensity I at the screen. On the positive-y side, point P lies between the third dark fringe and the third bright fringe after the central maximum. The resultant intensity at P is 3I. If the fringe width is β, what is the position of P measured from the central maximum?
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Question

In a Young's double-slit experiment, each slit individually produces intensity I at the screen. On the positive-y side, point P lies between the third dark fringe and the third bright fringe after the central maximum. The resultant intensity at P is 3I. If the fringe width is β, what is the position of P measured from the central maximum?

Options

G1 Physics · Accepted Answer

For equal slit intensities, I(resultant) = 4I cos²(πΔ ÷ λ). Given, I(resultant) = 3I. Thus the point is one-sixth of a fringe width away from a bright fringe. The third bright fringe is at 3β. The third dark fringe is at 5β ÷ 2. Since P lies between them, y(P) = 3β−β ÷ 6 = 17β ÷ 6. Correct option: A.