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A monochromatic light source emitting two wavelengths lambda₁ = 400 nm and lambda₂ = 600 nm is used in a Young's double-slit experiment. The fringe widths for lambda₁ and lambda₂ are beta₁ and beta₂ respectively. Within a distance y on one side of the central maximum, the numbers of fringes for lambda₁ and lambda₂ are m₁ and m₂ respectively. Which of the following statements is/are correct?

1. beta₂ > beta₁
2. m₁ > m₂
3. The 3rd bright fringe of lambda₂ from the centre coincides with the 5th dark fringe of lambda₁
4. The angular fringe width for lambda₁ is greater than for lambda₂

Correct answer: beta₂ > beta₁

Solution

beta = lambda*D/d. Since lambda₂ (600 nm) > lambda₁ (400 nm), beta₂ > beta₁ (A is correct). For m₁ and m₂: m = y/beta = yd/(lambda*D); since lambda₁ < lambda₂, m₁ > m₂ (B is also correct). For option C: 3rd maximum of lambda₂ is at y = 3*lambda₂*D/d = 1800D/d. 5th minimum of lambda₁ is at y = (5 - 1/2)*lambda₁*D/d = 4.5*400*D/d = 1800D/d. These match! (C is correct). Angular fringe width = lambda/d; lambda₁ < lambda₂ so angular fringe of lambda₁ is LESS than lambda₂ (D is false). Hence A, B, C are correct.

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