In Young’s double-slit experiment (using two coherent sources of the same intensity), the resultant intensity at a point on the screen is X, when the path difference is λ/3 (λ being the wavelength of light used). What will be the ratio of X and Y, where Y is the maximum resultant intensity?
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A.
Wed Mar 04 2026 00:00:00 GMT+0000 (Coordinated Universal Time)
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B.
Wed Apr 01 2026 00:00:00 GMT+0000 (Coordinated Universal Time)
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C.
Sun Feb 01 2026 00:00:00 GMT+0000 (Coordinated Universal Time)
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D.
Fri Apr 03 2026 00:00:00 GMT+0000 (Coordinated Universal Time)
Correct Answer:
B. Wed Apr 01 2026 00:00:00 GMT+0000 (Coordinated Universal Time)
Explanation:
In Young’s double-slit experiment, the intensity of light at any point on the screen is determined by the formula I = Imax * cos²(φ/2), where φ represents the phase difference. The relationship between phase difference (φ) and path difference (Δx) is φ = (2π/λ) * Δx. Given a path difference of λ/3, the phase difference is φ = (2π/λ) * (λ/3) = 2π/3 radians (or 120°). Substituting this into the intensity formula, the resultant intensity X is X = Y * cos²(120°/2) = Y * cos²(60°). Since cos(60°) = 1/2, X = Y * (1/2)² = Y/4. Therefore, the ratio of the resultant intensity X to the maximum intensity Y is X/Y = 1/4 or 1:4.
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